Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language 

20410581 
EXPERIMENTAL PHYSICS OF FUNDAMENTAL INTERACTIONS
(objectives)
The course provides the notions of experimental physics of elementary particles.
The course deals with both experimental and theoretical topics whose aim is to allow students to understand the experimental and theoretical path that led to the formulation of the Standard Model of fundamental interactions as we know it today. The fundamental experiments and discoveries starting from the discovery of elementary particles in cosmic rays up to the production of the vector bosons W and Z and of the Higgs boson are illustrated in detail. At the end of the course the student will have a broad view of particle physics from an experimental point of view, and sufficient knowledge of the theoretical tools necessary to understand its mechanisms. The course is supported by an exercise section whose aim is to reinforce the level of understanding of the topics covered and the calculation methods of the elementary processes, as well as allow students to apply the techniques learned for the calculation of some processes and the relationships between they exist. The course is aimed at all students and those who undertake a path of elementary particle physics that not, providing the basics of physics of elementary particles

DI MICCO BIAGIO
(syllabus)
Program:
(reference books)
1. Principles of invariance and conservation laws. 2. discrete and continuous symmetries; 3. relativistic equations: KleinGordon, Dirac 4. negative energy solutions, helicity, spin, solutions for zero mass, neutrinos 5. relativistic perturbation theory, interaction Hamiltonian, Feynman graphs, propagator as a Green function; 6. Lorentz transformations, laboratory and center of mass system, invariant mass, reaction kinematics, reaction threshold; 7. fields of interaction, Yukawa model; 8. primary and secondary cosmic rays, the muon: decay, mass and average life; 9. kinematics of decays, combination of angular moments, ClebschGordan coefficients, symmetry of the isospin; 10. decay widths and comparison between matrix elements, laws of storage; 11. phase spaction density, Scattering cross section, flux, factor of the space and of the invariant phases, scattering matrix elements; 12. the pion: charge, spin, parity, charge conjugation, isospin; 13. strange particles, hyperons, interaction of the K mesons; 14: strange baryons, mesonic and baryonic octets, SU (3) symmetry, hypercharge, Young's diagrams; 15: discovery of the antiproton, the antibaryons, the Delta resonance; 16: hadronic and mesonic resonances, model at Quarks; 17: representation of the mesons in the quarks model 18: potential scattering, solution of the Schroedingher equation for waves spherical; 19: diffusion and absorption cross section, unitarity limit, optical theorem; 20: resonant cross section, BreitWigner formula, baryon masses with GellMan Okubo formula; 21: the color quantum number, SU (3) representations of color, relationships between spin and SU (3) multiplets; 22: weak interaction, parity violation, madame Wu experiment; 23: oscillation of the K mesons, the Cabibbo angle, the GIM mechanism; 23: discovery of the charm and beauty quarks; 24: decay of D and B mesons, Feynman diagrams, isospin relations; 25: neutrino beams, neutrino flavor, discovery of the neutrino tau; 25: the accelerating machines e + e, hadronic impact section, the ratio R and the number of quarks and colors; 26: measurement of the helicity of the neutrino, discovery of the antineutrino; 27: deep inelastic scattering, parton distribution functions; 27: hadronic colliders, protonantiproton and protonproton: discovery of the W and Z bosons; 28: the Higgs boson 1. course notes, available on the course website;
2. F. Halzen, A. D. Martin, "An Introductory Course in Modern Particle Physics" 3. D. Scroeder, M. Peskin, "An Introduction to Quantum Field Theory" 4. S. Weinberg, "The Quantum Theory of Fields"

ORESTANO DOMIZIA
(syllabus)
Program:
(reference books)
1. Principles of invariance and conservation laws. 2. discrete and continuous symmetries; 3. relativistic equations: KleinGordon, Dirac 4. negative energy solutions, helicity, spin, solutions for zero mass, neutrinos 5. relativistic perturbation theory, interaction Hamiltonian, Feynman graphs, propagator as a Green function; 6. Lorentz transformations, laboratory and center of mass system, invariant mass, reaction kinematics, reaction threshold; 7. fields of interaction, Yukawa model; 8. primary and secondary cosmic rays, the muon: decay, mass and average life; 9. kinematics of decays, combination of angular moments, ClebschGordan coefficients, symmetry of the isospin; 10. decay widths and comparison between matrix elements, laws of storage; 11. phase spaction density, Scattering cross section, flux, factor of the space and of the invariant phases, scattering matrix elements; 12. the pion: charge, spin, parity, charge conjugation, isospin; 13. strange particles, hyperons, interaction of the K mesons; 14: strange baryons, mesonic and baryonic octets, SU (3) symmetry, hypercharge, Young's diagrams; 15: discovery of the antiproton, the antibaryons, the Delta resonance; 16: hadronic and mesonic resonances, model at Quarks; 17: representation of the mesons in the quarks model 18: potential scattering, solution of the Schroedingher equation for waves spherical; 19: diffusion and absorption cross section, unitarity limit, optical theorem; 20: resonant cross section, BreitWigner formula, baryon masses with GellMan Okubo formula; 21: the color quantum number, SU (3) representations of color, relationships between spin and SU (3) multiplets; 22: weak interaction, parity violation, madame Wu experiment; 23: oscillation of the K mesons, the Cabibbo angle, the GIM mechanism; 23: discovery of the charm and beauty quarks; 24: decay of D and B mesons, Feynman diagrams, isospin relations; 25: neutrino beams, neutrino flavor, discovery of the neutrino tau; 25: the accelerating machines e + e, hadronic impact section, the ratio R and the number of quarks and colors; 26: measurement of the helicity of the neutrino, discovery of the antineutrino; 27: deep inelastic scattering, parton distribution functions; 27: hadronic colliders, protonantiproton and protonproton: discovery of the W and Z bosons; 28: the Higgs boson 1. course notes, available on the course website;
2. F. Halzen, A. D. Martin, "An Introductory Course in Modern Particle Physics" 3. D. Scroeder, M. Peskin, "An Introduction to Quantum Field Theory" 4. S. Weinberg, "The Quantum Theory of Fields" 
8  FIS/01  64  16      Core compulsory activities  ITA 
20401904 
THEORETICAL PHYSICS I
(objectives)
To study classical electrodynamics in detail, to provide the elements of relativistic quantum mechanics. Provide the basics of field theory and QED

DEGRASSI GIUSEPPE
(syllabus)
Special Relativity and Electromagnetism.
(reference books)
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and controvariant vectors, tensors, transformation law of the fields. Relativistic Dynamics: fourvelocity, fourmomentum, Minkowski force. Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields, electromagnetic field tensor, covariant formulation of the Maxwell equations, fourpotential, gauge invariance. Conservation laws: Maxwell stress tensor, energymomentum tensor, conservation of energy, momentum and angular momentum. Solution of the Maxwell equations for the fourpotential in the vacuum in the Lorentz gauge. Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect. Cerenkov effect. Relativistic Quantum Mechanics KleinGordon equation. Dirac equation, nonrelativistic limit. Covariance of the Dirac equation. Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality. Quantum Field Theory Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators. Heisenberg representation. Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization. Electromagnetic field, covariant quantization. Global and local invariance. Interaction picture. Smatrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields. Quantzation of the electromagnetic field. Feynman diagrams and rules in QED. Treelevel processes: e+e  mu+ mu, scattering by an external field. V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Sanfilippo Francesco
(syllabus)
Special Relativity and Electromagnetism.
(reference books)
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and controvariant vectors, tensors, transformation law of the fields. Relativistic Dynamics: fourvelocity, fourmomentum, Minkowski force. Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields, electromagnetic field tensor, covariant formulation of the Maxwell equations, fourpotential, gauge invariance. Conservation laws: Maxwell stress tensor, energymomentum tensor, conservation of energy, momentum and angular momentum. Solution of the Maxwell equations for the fourpotential in the vacuum in the Lorentz gauge. Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect. Cerenkov effect. Relativistic Quantum Mechanics KleinGordon equation. Dirac equation, nonrelativistic limit. Covariance of the Dirac equation. Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality. Quantum Field Theory Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators. Heisenberg representation. Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization. Electromagnetic field, covariant quantization. Global and local invariance. Interaction picture. Smatrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields. Quantzation of the electromagnetic field. Feynman diagrams and rules in QED. Treelevel processes: e+e  mu+ mu, scattering by an external field. V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons. 
8  FIS/02  46  22      Core compulsory activities  ITA 
20402210 
CONDENSED MATTER PHYSICS
(objectives)
The course aims to apply the methods of mechanics quantum to the description of the fundamental properties of solid matter

GALLO PAOLA
(syllabus)
Overview on condensed matter. Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: xrays, electrons and neutrons. Quasicrystals. Classification of crystalline solids and bonds. Adiabatic approximation (BornOpenheimer). Lattice vibrational dynamics, phonons. Specific heats of Einstein, Debye and electronic. Electrons in periodic potentials: the Bloch theorem. Theory of the free electron in metals. The many electrons Hamiltonian and one electron approximations: Hartree and Hartree Fock equation. Band theory in crystals: Tight Binding method and the nearly free electron approximation. Electronic properties of relevant crystals. Transport in metals. Intrinsic and doped semiconductors and transport. pn junction. Superconductivity.
(reference books)
Giuseppe Grosso and Giuseppe Pastori Parravicini Solid State Physics Academic Press
others: Neil W. Ashcroft N. David Mermin Solid State Physics Saunders College Charles Kittel Introduzione alla Fisica Dello Stato Solido Casa Editrice Ambrosiana WRITTEN NOTES, PRESENTATIONS AND EXERCISES will be published on the course web site http://webusers.fis.uniroma3.it/~gallop/

LUPI LAURA
(syllabus)
Exercises on the following topics:
(reference books)
Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: xrays. Quasicrystals. Lattice vibrational dynamics, phonons. Specific heats of Einstein, Debye and electronic. Band theory of electrons in crystals: Tight Binding method and the nearly free electron approximation. Intrinsic and doped semiconductors and transport. EXERCISES published on the webpage of the class.
Exams of previous years available on the same webpage. 
8  FIS/03  60  20      Core compulsory activities  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language 

20402211 
COMPLEMENTS OF MATHEMATICAL METHODS FOR PHYSICS
(objectives)
The aim of the course is to learn the basic tools to deal with Lie algebras and their representations and to acquire computer calculation techniques,both for symbolic and for numerical calculations. Topics of the course
will be dealt with using either Wolfram Language and Python or alternative computer languages preferred by the student.

FRANCESCHINI ROBERTO
(syllabus)
Group Theory (CA)
(reference books)
SU(2) and SU(3) The Killing Form Simple Lie Algebras Representations Simple Roots and the Cartan Matrix The Classical Lie Algebras The Exceptional Lie Algebras Casimir Operators and Freudenthal’s Formula The Weyl Group Weyl’s Dimension Formula Reducing Product Representations Subalgebras Branching Rules Numerical Methods Refresh on Probability and Random variables Refresh on Measurement, uncertainty and its propagation Refresh on Curvefitting, leastsquares, optimization Classical numerical integration, speed of convergence Integration MC (Mean, variance) Sampling Strategies Applications Propagation of uncertainties Generation according to a distribution Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html Robert Cahn  SemiSimple Lie Algebras and Their Representations  Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S.  Introduction to Monte Carlo methods arXiv:hepph/0006269 Taylor, J.  An introduction to error analysis  University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre Dubi, A.  Monte Carlo applications in systems engineering  Wiley Disponibile nella biblioteca Scientifica di Roma Tre readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html 
6  FIS/02  34  18      Core compulsory activities  ITA 
20410086 
ELEMENTI DI RELATIVITA' GENERALE, ASTROFISICA E COSMOLOGIA
(objectives)
The course aims to provide students with the basic concepts of general relativity and its applications to physical systems, with particular reference to compact objects (black holes), gravitational waves and the universe

BRANCHINI ENZO FRANCO
(syllabus)
 SPECIAL RELATIVITY. VECTORS AND TENSORS. METRIC TENSOR. ENERGYMOMENTUM TENSOR.
(reference books)
 GENERAL RELATIVITY. UNDERLYING CONCEPTS. AFFINE CONNECTION. PARALLEL TRANSPORT. GEODESICS EQUATION.  SYMMETRY AND KILLING VECTORS. RIEMANN TENSOR. SINGULARITY.  EINSTEIN EQUATIONS.  SCHWARZSCHILD METRIC.  ORBITS IN THE SCHWARZSCHILD METRIC. MERCURY’S ORBIT.  NON ROTATING BLACK HOLES. EVENT HORIZON AND THE CHOICE OF COORDINATES.  KERR METRIC. ROTATING BLACK HOLES AND FRAME DRAGGING.  INTRODUCTION TO GRAVITATIONAL WAVES.  THE COSMOLOGICAL PRINCIPLE AND ROBERTSONWALKER METRIC.  FRIEDMAN EQUATIONS. NEWTONIAN LIMIT.  COSMOLOGICAL REDSHIFT. COSMOLOGICAL HORIZONS. COMOVING COORDINATES AND PROPER DISTANCE.  LUMINOSITY DISTANCE. ANGULAR DIAMETER DISTANCE.  OBSERVATIONAL TESTS: HUBBLE TEST, ANGULAR DIAMETER TEST, NUMBER COUNTS.  FLUIDS RELEVANT IN COSMOLOGY: EQUATION OF STATE AND DENSITY EVOLUTION. Cosmological constant.  THE EQUIVALENCE EPOCH.  THERMAL HISTORY OF THE UNIVERSE: DECOUPLING. RECOMBINATION.  MATTER/ANTIMATTER AND THE BARYON ASYMMETRY.  PLANCK EPOCH AND QUANTUM GRAVITY.  HORIZON PARADOX. FLATNESS PARADOX. INFLATIONARY SOLUTION. COSMIC INFLATION.  DARK MATTER.  A BRIEF HISTORY OF THE UNIVERSE. HADRONIC EPOCH. LEPTONIC EPOCH. RADIATIVE EPOCH.  NEUTRINO DECOUPLING.  COSMOLOGICAL NUCLEOSYNTHESIS. MATTER EPOCH. FIRST OBJECTS. REIONIZATION.  INHOMOGENEITY AND ANISOTROPY. JEANS GRAVITATIONAL INSTABILITY AND THE GROWTH OF COSMIC STRUCTURES Carroll S. Spaceitme Geometry [Pearson 2003]
Coles P., Lucchin F. Cosmology [Wiley 2000] Kolb E., Turner M. The eraly Universe [Addison Wesley 1990] 
6  FIS/05  48        Core compulsory activities  ITA 
20410041 
ASTROFISICA GENERALE
(objectives)
Provide the student with a complete overview of the fundamental physical processes underlying Astrophysics

BIANCHI STEFANO
(syllabus)
Radiative processes in Astrophysics: Transfer Equation, Bremsstrahlung, Synchrotron Emission, Inverse Compton Effect, Pairs Production, Cherenkov Effect
(reference books)
Nuclear Interactions, Nuclear Lines Spectroscopy: Spectroscopic Notation, Energy Levels, Selection Rules, Ionization Balance, Emission and Absorption Lines, Density and Temperature Measures, Dust and Extinction Molecular Spectroscopy Other Messengers in Astrophysics: Gravitational Waves, Neutrinos Particle Acceleration: Fermi Mechanisms, Shocks (LONGAIR MALCOM S. ) HIGH ENERGY ASTROPHYSICS 3RD ED. [CAMBRIDGE 2011]
(G.B. RYBICKI, A.P. LIGHTMAN) RADIATIVE PROCESSES IN ASTRIPHYSICS [WILEY] (SHAPIRO S.L, TEUKOLSKY S.A.) BLACK HOLES, WHITE DWARFS AND NEUTRON STARS [WILEY] G. Ghisellini “Radiative Processes in High Energy Astrophysics”, 2013 
6  FIS/05  60        Core compulsory activities  ITA 
20401878 
EXTRAGALACTIC ASTROPHYSICS
(objectives)
The course aims to provide the student with the basic concepts of astrophysics of our Galaxy and external galaxies

LA FRANCA FABIO
(syllabus)
1.
(reference books)
Principles of Stellar Evolution 2. Principles of Observational Astronomy 3. The Milky Way 4. The central Black Hole of the Milky Way 5. Galaxy classification 6. Mass distribution, potentials, and isophotes 7. Rotation curves 8. Scaling relations in galaxies 9. Astrophysical Spectroscopy: cold gas, hot gas and molecular gas 10. Velocity, temperature and density measures 11. Active Galactic Nuclei: the structure and the central engine 12. The measure of the supermassive black hole masses 13. The evolution of the Active Galactic Nuclei 14. AGN/galaxy coevolution 15. Measure and history of the Star Formation Rate of galaxies 16. Luminosity and mass functions evolution of AGN and galaxies. Synthesis of the cosmic backgrounds. 17. Metallicity 18. Clusters of galaxies Testo: L.S. Sparke and J.S. Gallagher
Galaxies in the Universe  An Introduction. Cambridge University Press 
6  FIS/05  60        Core compulsory activities  ITA 
20402214 
ASTROPHYSICS OF STARS
(objectives)
Provide the student with a good knowledge of stellar structure and evolution, with applications relevant to general astrophysical problems, such as star dating and the age of the Universe, the role of the abundance of light elements of evolution and the connection with cosmological abundances , the variable stars and the supernovae, and their role for the determination of the distance scale, the compact objects (white dwarfs, neutron stars and their importance in the evolution of interactive binary. The aim is therefore to provide the basis knowledge about the stars for astrophysical applications, even not stellar

VENTURA PAOLO
(syllabus)
Stellar Observations
(reference books)
Magnitude of a star. Brightness intensity. Apparent and relative magnitude. Black body spectrum. Wien and StefanBoltzmann laws. The colors of stars. Optical Depth. Radiation transport equation. EddingtonBarbier approximation. Gray atmosphere. Definition of photosphere and effective temperature. HertzprungRussell and ColorMagnitude diagrams. Stellar spectra. Saha and Boltzman equations. Hydrogen lines. Balmer's discontinuity. Spectral Types. Radiation and opacity transport. Electromagnetic radiation. Relation between energy radial flux and temperature gradient. Opacity and free path of photons. Rosseland's average opacity coefficient. Photon absorption mechanisms: boundbound, , boundfree, and freefree. Kramer's opacity. Thomson scattering. Electronic conduction. Relative importance of the various types of opacity in the densitytemperature plan. Convection in the stars. Convective instability. Schwarzschild and Ledoux criteria for convective instability. Main causes for establishing convective instability. Convection efficiency. The "Mixing Length Theory" and the free parameter alpha. Convectionrelated uncertainties. Free parameter calibration. Problems related to turbulence and nonlocal nature of convection. State equation Equation of state for stellar interiors. Ideal gas and radiation pressures. Electron degeneracy. The role of the Pauli Principle. The Fermi momentum. Partial and complete degeneracy. Equation of state for degenerate gas in the relativistic and nonrelativistic case. Crystallization. Neutronization. Relative importance of the various types of pressure in the densitytemperature plane. Generation of nuclear energy Nuclear reactions. Mass defect. Tunnel effect. Resonances. Cross sections. Rate of nuclear reactions. Nuclear energy generation coefficient. Gamow Peak. Functional dependence of the rate of nuclear reactions on the temperature. Electrons screening. The protonproton chain. The CNO cycle and the relative equilibrium. The 3α reactions. The equations of stellar structure Equilibrium equations of the star. Mass Conservation. Expression and physical significance of the gravitational energy generation coefficient. Energy conservation. Hydrostatic balance. Energy transport. Neutrinos energy. Treatment of atmospheric layers. Stellar structure equations in adimensional form. The birth of the stars and early evolutionary phases The Virial theorem. Jeans criterion for collapse. The Jeans mass. Hierarchical fragmentation. Radiative cooling. Isothermal and adiabatic collapse. Accretion disks and disk structure. Energy balance during the accretion phase. Protostars. Hayashi theory for premain sequence stars. Hayashi lines and their physical meaning. Stratification of entropy into radiative and convective stars. Premain sequence evolutionary tracks in the HR diagram. The KelvinHelmotz time scale. The Palla & Stahler model. Evolution of the core in hydrostatic equilibrium. The "birthline”. Pre main sequence lithium burning. Lithium in stars belonging to young associations. The mass limit for the ignition of hydrogen burning. Brown dwarfs and giant planets. The role of electronic degeneracy. "Disklocking" and magnetic braking. Core hydrogen burning Main sequences (MS) of open and globular clusters. MassLuminosity relation for MS stars. The shape of the Zero Age Main Sequence (ZAMS). Lower and upper limit for the mass of MS stars. Structure of MS stars of different mass: the extension of convective and radiative zones. Mass limit for proton  proton and CNO burning. The role of the formation of molecular hydrogen in the external regions of the stars on the ZAMS Morphology. Main sequences observed in globular and open clusters: interpretation. Evolutionary tracks of main sequence stars. Theoretical uncertainties about the evolution of MS stars: overshooting from the core, temperature gradient in convective envelopes. The red giant stage PostMS evolution. Giant expansion. The SchonbergChandrasekhar instability. Degeneracy of the helium core in low mass models. First dredgeup: causes and effects. Extension of the convective envelope of the stars according to the effective temperature. Luminosity functions. Bump of the luminosity function during the giant phase. Evolution of lowmass stars up to the red giant tip. The role of the CNO shell. Core mass  luminosity relationship for lowmass stars. The role of neutrinos for the determination of the temperature peak. Helium Flash. Flash thermodynamics. The role of electron degeneracy. Miniflash episodes. Comparison of pre and postflash thermodynamic structures. Horizontal branch evolution: evolutionary tracks towards the blue and the red side of the HR diagram. The role of helium. Interpretation of the horizontal branches of globular clusters: the role of age and mass loss. Helium burning in non degenerate stars. "Blue loop" in the HR diagram. Asymptotic branch evolution Second dredgeup. Degeneracy of carbon and oxygen core. Double shell nuclear burning. Thermal instability of the thermal pulse. Asymptotic Giant branch evolution. Luminosity  core mass relationship for AGB Stars. "Hot Bottom Burning" and Third Dredgeup. Llithiumrich stars. Carbon stars. Changes in the surface chemistry of AGB stars of different mass. SuperAGB evolution: Convective flame and the formation of a core of Oxygen and Neon. Dust production during the asymptotic giant branch phase. Interpretation of the observational diagrams of evolved stellar populations in the Magellanic Clouds. White dwarf Late stages of evolution of stars of small or intermediate mass. The Planetary Nebula evolution. Chandrasekhar's theory for white dwarf stars. Structural properties of white dwarfs: massradius relationship. Energy balance of white dwarfs. Luminosity of White Dwarfs. Cooling theory. Variable stars Stellar variability: historical introduction. Radial oscillations. Period of propagation of an acoustic perturbation. The comparison between variable stars and thermal machines. Mechanisms ε and k for the production of the ‘driving’ mechanism of pulsations. Hydrogen and helium partial ionization zones as drivers of star variability. Distribution of variable stars in the HR diagram, and its interpretation. Strips of instability. Cepheid and RR Lyrae Variables: Evolutionary Stage, and PeriodLuminosity relationships. Stellar clusters The spatial distribution of stellar clusters across the Milky Way. Distribution of stars in clusters in the colormagnitude plane. Differences between open and globular clusters. The isochrone fitting method: turnoff magnitude as distance and age indicator. Reddening and extinction. Impact of metallicity on the color of the main sequence of star clusters. Interpretation of the horizontal branches of globular clusters. Chemical anomalies in globular clusters stars. Oxygensodium and magnesiumaluminum anticorrelations. Photometric evidence of the presence of one or more stellar components enriched in helium. The AGB scenario for the formation of multiple populations in globular clusters. Massive stars evolution The final stages of the evolution of massive stars: LBV and WolfRayet stars. Supernovae: Supernovae observations of types Ia, Ib, Ic and II. Postcarbon evolutionary phases: formation of a degenerate core. Collapse of the core. Core photodisintegration .Explosive Mechanisms. Title: Stellar structure and evolution
Authors: Kippenhahn, Weigert SpringerVerlag 1990 Title: Introduction to stellar Astrophysics (vol. 2) Author: E. BohmVitense Cambridge University Press 1992 Title: Introduction to stellar Astrophysics (vol. 3) Author: E. BohmVitense Cambridge University Press 1992 
6  FIS/05  48        Core compulsory activities  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  

20402143 
COSMOLOGY
(objectives)
The course aims to explore in detail some aspects of Modern Cosmology which are just as many topics of high interest both from the point of view of the physical phenomena involved and from the point of view of the methodologies used. Particular attention is paid to the comparison between observations and theory, that is to the relation between the Cosmology and the Astrophysical Astrophysics.

BRANCHINI ENZO FRANCO
(syllabus)
This course discusses in detail the key issues in Modern Cosmology, including outstanding problems. The goal is to provide an overview of the subject and to illustrate the main techniques, theoretical and observational alike, commonly used in this field. The main topics are:
(reference books)
 Density fluctuation in a cosmological scenario: generation and growth. Gravitational Instability. Newtonian limit and the Jeans Theory. Linear theory.  Cosmic Microwave Background temperature fluctuation. Acoustic peaks. The SachsWolfe effect. Secondary effects.   Cosmic backgrounds in different energy bands: Radio, Xray and gammaray  Secondary anisotropies. The GunnPeterson effect, cosmic reionization, Lyalpha forest and SunayevZel'dovich effect.  The intergalactic medium at low redshift and the missing baryons problem.  Large scale structures. Statistical analysis of the galaxy distribution in space. Correlation functions and power spectra.  Luminous vs. dark matter. Galaxy bias.  Nonlinear growth of density fluctuations. The Zel'dovich approximation. The spherical collapse model. The halo model. PressSchechter theory and its extension.  Peculiar velocities, distance indicators and their calibrations.  Gravitational lensing: Theory and observations. Microlensing. Strong lensing. Weak lensing. Peacock J. Physical Cosmology. Cambridge Univ.Press
Longair M. Galaxy Formation [A&A Library ] Coles P., Lucchin F. Cosmology [Wiley 2000] Various reviews provided during the course. 
8  FIS/05  72        Related or supplementary learning activities  ITA  
20402146 
HIGH ENERGY ASTROPHYSICS
(objectives)
Provide the student with an overview of the main phenomena in the field of High Energy Astrophysics, with particular attention to growth phenomena on compact objects (white dwarfs, neutron stars and black holes) and to particle acceleration phenomena

BIANCHI STEFANO
(syllabus)
COMPACT OBJECTS: WHITE DWARFS, NEUTRON STARS, THE CHANDRASEKHAR LIMIT, PULSARS, BLACK HOLES
(reference books)
ACCRETION: THEORY, EDDINGTON LIMIT, ACCRETION DISKS XRAY BINARIES: CLASSIFICATION AND PHENOMENOLOGY, CATACLYSMIC VARIABLES, LOWMASS AND HIGHMASS XRAY BINARIES, BLACK HOLE CANDIDATES ACTIVE GALACTIC NUCLEI: CLASSIFICATION AND PHENOMENOLOGY, XRAY AND GAMMARAY EMISSION, JETS, SUPERLUMINAL MOTIONS GAMMA RAY BURSTS: PHENOMENOLOGY, ORIGIN, EMISSION MECHANISMS CLUSTER OF GALAXIES: EMISSION FROM THE INTERGALACTIC MEDIUM, COOLING FLOWS COSMIC RAYS: COMPOSITION, SPECTRUM AND ORIGIN, SUPERNOVA REMNANTS, ULTRA HIGH ENERGY COSMIC RAYS (LONGAIR MALCOM S. ) HIGH ENERGY ASTROPHYSICS 3RD ED. [CAMBRIDGE 2011]
(KIPPENHAHN R., WEIGERT A.) STELLAR STRUCTURE AND EVOLUTION [SPRINGER 1994] (G.B. RYBICKI, A.P. LIGHTMAN) RADIATIVE PROCESSES IN ASTRIPHYSICS [WILEY] (VIETRI M.) ASTROFISICA DELLE ALTE ENERGIE [BORINGHIERI] (SHAPIRO S.L, TEUKOLSKY S.A.) BLACK HOLES, WHITE DWARFS AND NEUTRON STARS [WILEY] 
6  FIS/05  60        Related or supplementary learning activities  ITA  

Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  



20402228 
TRAINING
(objectives)
The internship / stage activity is a work that the student carries out under the guidance of a lecturer both in the university field, and in external sites affiliated with the University; provides the student with the ability to synthesize the acquired global knowledge, applying it to the drafting and elaboration of the thesis work

6          Other activities  ITA  
20410392 
Lingua inglese
(objectives)
Level B2 provides the student with a more indepth ability to communicate the conclusions, as well as the knowledge underlying them, of what has been learned, clearly and critically, also through the use in written and oral form of the English language and disciplinary lexicons, if necessary using the IT tools necessary for the presentation, acquisition and exchange of scientific data also through written documents, diagrams and diagrams. Ability to support a scientific discussion using the topics learned.

4  40        Other activities  ITA  
20401594 
FINAL EXAM
(objectives)
Demonstration by the student of the ability to deal with specific scientific problems, research and / or application of the concepts learned in the various disciplines of Physics

30          Final examination and foreign language test  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language 

20410581 
EXPERIMENTAL PHYSICS OF FUNDAMENTAL INTERACTIONS
(objectives)
The course provides the notions of experimental physics of elementary particles.
The course deals with both experimental and theoretical topics whose aim is to allow students to understand the experimental and theoretical path that led to the formulation of the Standard Model of fundamental interactions as we know it today. The fundamental experiments and discoveries starting from the discovery of elementary particles in cosmic rays up to the production of the vector bosons W and Z and of the Higgs boson are illustrated in detail. At the end of the course the student will have a broad view of particle physics from an experimental point of view, and sufficient knowledge of the theoretical tools necessary to understand its mechanisms. The course is supported by an exercise section whose aim is to reinforce the level of understanding of the topics covered and the calculation methods of the elementary processes, as well as allow students to apply the techniques learned for the calculation of some processes and the relationships between they exist. The course is aimed at all students and those who undertake a path of elementary particle physics that not, providing the basics of physics of elementary particles

Derived from
20410581 FISICA SPERIMENTALE DELLE INTERAZIONI FONDAMENTALI in Fisica LM17 DI MICCO BIAGIO, ORESTANO DOMIZIA
(syllabus)
Program:
(reference books)
1. Principles of invariance and conservation laws. 2. discrete and continuous symmetries; 3. relativistic equations: KleinGordon, Dirac 4. negative energy solutions, helicity, spin, solutions for zero mass, neutrinos 5. relativistic perturbation theory, interaction Hamiltonian, Feynman graphs, propagator as a Green function; 6. Lorentz transformations, laboratory and center of mass system, invariant mass, reaction kinematics, reaction threshold; 7. fields of interaction, Yukawa model; 8. primary and secondary cosmic rays, the muon: decay, mass and average life; 9. kinematics of decays, combination of angular moments, ClebschGordan coefficients, symmetry of the isospin; 10. decay widths and comparison between matrix elements, laws of storage; 11. phase spaction density, Scattering cross section, flux, factor of the space and of the invariant phases, scattering matrix elements; 12. the pion: charge, spin, parity, charge conjugation, isospin; 13. strange particles, hyperons, interaction of the K mesons; 14: strange baryons, mesonic and baryonic octets, SU (3) symmetry, hypercharge, Young's diagrams; 15: discovery of the antiproton, the antibaryons, the Delta resonance; 16: hadronic and mesonic resonances, model at Quarks; 17: representation of the mesons in the quarks model 18: potential scattering, solution of the Schroedingher equation for waves spherical; 19: diffusion and absorption cross section, unitarity limit, optical theorem; 20: resonant cross section, BreitWigner formula, baryon masses with GellMan Okubo formula; 21: the color quantum number, SU (3) representations of color, relationships between spin and SU (3) multiplets; 22: weak interaction, parity violation, madame Wu experiment; 23: oscillation of the K mesons, the Cabibbo angle, the GIM mechanism; 23: discovery of the charm and beauty quarks; 24: decay of D and B mesons, Feynman diagrams, isospin relations; 25: neutrino beams, neutrino flavor, discovery of the neutrino tau; 25: the accelerating machines e + e, hadronic impact section, the ratio R and the number of quarks and colors; 26: measurement of the helicity of the neutrino, discovery of the antineutrino; 27: deep inelastic scattering, parton distribution functions; 27: hadronic colliders, protonantiproton and protonproton: discovery of the W and Z bosons; 28: the Higgs boson 1. course notes, available on the course website;
2. F. Halzen, A. D. Martin, "An Introductory Course in Modern Particle Physics" 3. D. Scroeder, M. Peskin, "An Introduction to Quantum Field Theory" 4. S. Weinberg, "The Quantum Theory of Fields" 
8  FIS/01  64  16      Core compulsory activities  ITA 
20401904 
THEORETICAL PHYSICS I
(objectives)
To study classical electrodynamics in detail, to provide the elements of relativistic quantum mechanics. Provide the basics of field theory and QED

Derived from
20401904 FISICA TEORICA I in Fisica LM17 N0 DEGRASSI GIUSEPPE, Sanfilippo Francesco
(syllabus)
Special Relativity and Electromagnetism.
(reference books)
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and controvariant vectors, tensors, transformation law of the fields. Relativistic Dynamics: fourvelocity, fourmomentum, Minkowski force. Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields, electromagnetic field tensor, covariant formulation of the Maxwell equations, fourpotential, gauge invariance. Conservation laws: Maxwell stress tensor, energymomentum tensor, conservation of energy, momentum and angular momentum. Solution of the Maxwell equations for the fourpotential in the vacuum in the Lorentz gauge. Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect. Cerenkov effect. Relativistic Quantum Mechanics KleinGordon equation. Dirac equation, nonrelativistic limit. Covariance of the Dirac equation. Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality. Quantum Field Theory Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators. Heisenberg representation. Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization. Electromagnetic field, covariant quantization. Global and local invariance. Interaction picture. Smatrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields. Quantzation of the electromagnetic field. Feynman diagrams and rules in QED. Treelevel processes: e+e  mu+ mu, scattering by an external field. V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons. 
8  FIS/02  46  22      Core compulsory activities  ITA 
20402210 
CONDENSED MATTER PHYSICS
(objectives)
The course aims to apply the methods of mechanics quantum to the description of the fundamental properties of solid matter

Derived from
20402210 FISICA DELLA MATERIA CONDENSATA in Fisica LM17 N0 GALLO PAOLA, LUPI LAURA
(syllabus)
Overview on condensed matter. Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: xrays, electrons and neutrons. Quasicrystals. Classification of crystalline solids and bonds. Adiabatic approximation (BornOpenheimer). Lattice vibrational dynamics, phonons. Specific heats of Einstein, Debye and electronic. Electrons in periodic potentials: the Bloch theorem. Theory of the free electron in metals. The many electrons Hamiltonian and one electron approximations: Hartree and Hartree Fock equation. Band theory in crystals: Tight Binding method and the nearly free electron approximation. Electronic properties of relevant crystals. Transport in metals. Intrinsic and doped semiconductors and transport. pn junction. Superconductivity.
(reference books)
Giuseppe Grosso and Giuseppe Pastori Parravicini Solid State Physics Academic Press
others: Neil W. Ashcroft N. David Mermin Solid State Physics Saunders College Charles Kittel Introduzione alla Fisica Dello Stato Solido Casa Editrice Ambrosiana WRITTEN NOTES, PRESENTATIONS AND EXERCISES will be published on the course web site http://webusers.fis.uniroma3.it/~gallop/ 
8  FIS/03  60  20      Core compulsory activities  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language 

20402211 
COMPLEMENTS OF MATHEMATICAL METHODS FOR PHYSICS
(objectives)
The aim of the course is to learn the basic tools to deal with Lie algebras and their representations and to acquire computer calculation techniques,both for symbolic and for numerical calculations. Topics of the course
will be dealt with using either Wolfram Language and Python or alternative computer languages preferred by the student.

Derived from
20402211 COMPLEMENTI DI METODI MATEMATICI DELLA FISICA in Fisica LM17 N0 FRANCESCHINI ROBERTO
(syllabus)
Group Theory (CA)
(reference books)
SU(2) and SU(3) The Killing Form Simple Lie Algebras Representations Simple Roots and the Cartan Matrix The Classical Lie Algebras The Exceptional Lie Algebras Casimir Operators and Freudenthal’s Formula The Weyl Group Weyl’s Dimension Formula Reducing Product Representations Subalgebras Branching Rules Numerical Methods Refresh on Probability and Random variables Refresh on Measurement, uncertainty and its propagation Refresh on Curvefitting, leastsquares, optimization Classical numerical integration, speed of convergence Integration MC (Mean, variance) Sampling Strategies Applications Propagation of uncertainties Generation according to a distribution Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html Robert Cahn  SemiSimple Lie Algebras and Their Representations  Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S.  Introduction to Monte Carlo methods arXiv:hepph/0006269 Taylor, J.  An introduction to error analysis  University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre Dubi, A.  Monte Carlo applications in systems engineering  Wiley Disponibile nella biblioteca Scientifica di Roma Tre readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html 
6  FIS/02  34  18      Core compulsory activities  ITA 
20410020 
COMPLEMENTI DI FISICA DELLA MATERIA CONDENSATA
(objectives)
Give the student a thorough understanding of the structural and electronic properties of solids, their transport properties, the response to electromagnetic fields

DE SETA MONICA
(syllabus)
Electronic properties of selected crystals
(reference books)
Reminds on band structure calculation methods. Electronic structure of molecular and ionic solids. Band structure of IIVI, IIIV systems and of covalent crystals with diamond structure. Impurity levels in doped semiconductors. Internal energy, pressure and compressibility of an electron gas. Band structures and Fermi surfaces of selected metals. Transport properties: The Drude Model. Semiclassical Equations of transport. Boltzmann equation. Electron phonon interaction. Relaxation time approximation. Static and dynamic electrical conductivity in metals. Thermoeletrictic power and thermal conductivity. Transport in homogeneous and doped semiconductors. Drift and diffusion currents. Generation and recombination of electronhole pairs in semiconductors. Continuity equation. Recombination times and diffusion length. Current voltage characteristics of the pn junction. Metalsemiconductor junction. Schottky Diode, Field Effect Transistors. Optical properties of solids Maxwell Equations in solids. Complex Dielectric Constant. Kramers Kronig Relations. Lorentz Oscillator. Absorption and reflection coefficients. The Drude theory of the optical properties of metals. Optical properties of semiconductors and insulators. Direct interband transitions and critical points. Optical constants of Ge and Graphite. Absorption from impurity levels. Exciton effects. Indirect phononassisted transitions. Twophoton absorption. Raman Scattering. Optical phonon absorption. Emission, Photoluminescence, Electroluminesce, solid state LEDs and Lasers. Electron gas in magnetic fields Energy levels and density of states of a free electron gas in a magnetic fields. Orbital magnetic susceptibility and Haasvan Alphen effect. Magnetoresistivity and classical Hall effect. Phenomenology of the quantum Hall effect. Magnetic properties of matter. Quantum mechanical treatment of magnetic suscectibility. Pauli paramagnetism. Magnetic suscectibility of closedshell systems. Permanent magnetic dipoles in atoms and ions with partially filled shells. Paramagnetism of localized magnetic moments. Curie and Van Vleck paramagnetism. Magnetic ordering in crystals. Mean field theory of ferromagnetism: Weiss model. CurieWeiss law. Critical temperature in ferromagnetic materials. Ferromagnetism, exchange interaction and Heisemberg model. Microscopic origin of the coupling between localized magnetic moments. Dipolar interaction and magnetic domains. AshcroftMermin: "Solid State Physics"
GrossoPastoriParravicini: "Solid State Physics" Sze Physics of Semiconductor Devices 
9  FIS/03  72        Core compulsory activities  ITA 
20410022 
Quantum Theory of Matter
(objectives)
To offer an introduction to the methods of field theory applied to the study of manybody systems of Matter Physics. The course program includes in the first part the study of the perturbative methods and the theory of linear response applied to the electron gas with the use of Green functions and Feynman diagrams. In the second part the theoretical study of the quantum phenomena that characterize matter at low temperatures such as superfluidity and superconductivity is developed

RAIMONDI ROBERTO
(syllabus)
 Fluctuationdissipation theorem and linear response theory.
(reference books)
Green functions at zero temperature. Lehmann decomposition. Analytical properties.  Perturbative development and Feynman diagrams. Dyson equation.  Green functions at finite temperature: Matsubara technique.  HartreeFock theory and RPA approximation. ThomasFermi screen. Lindhard function. Fermi liquid theory.  Phenomenology of superfluidity. Landau theory. Microscopic theory of superfluidity. Bogolubov theory.  Phenomenology of superconductivity.  Microscopic BCS theory of superconductivity. Gorkov's derivation of the LandauGinzburg equations. Theory of electronic transport in disordered systems. 1 Carlo Di Castro, Roberto Raimondi, Statistical Mechanics and Applications in Condensed Matter, Cambridge University Press 2015.
2 Piers Coleman, Introduction to ManyBody Physics, Cambridge University Press 2015. 
8  FIS/03  80        Core compulsory activities  ITA 
20410583 
FUNDAMENTALS OF MICROSCOPY WITH LABORATORY
(objectives)
Provide the theoretical foundations and the experimental practice of microscopic techniques with particular reference to optical, electronic and probe microscopy.

CAPELLINI GIOVANNI
(syllabus)
Eye and perception. History of microscopy.
(reference books)
Light optics. Fundamentals of optical microscopy. Resolution, contrast and magnification. The components of an optical microscope. Image formation. Reflection microscopy. Phase contrast. Bright field and dark field. Polarization. Principles of operation of scanning electron microscopy (SEM). Components of a SEM. Sampleprobe interaction. Detection of secondary and backscattered electrons. Use of the SEM. Principles of operation and components of a scanning probe microscope (SPM). Tunnel effect microscopy (STM). Atomic force microscopy (AFM). AFM in contact. AFM in no contact. Secondary scanning techniques. Resolution and artifacts. Introduction to 2D and 3D image analysis, improvement of image quality with and without the use of kernel, segmentation, binarization and quantitative image analysis with openaccess software. Notes based on the slides used during the lectures.
Fundamentals of Light Microscopy and Electronic Imaging. D. B. Murphy , M. W. Davidson. J. Wiley & Sons Scanning Microscopy for Nanotechnology, W. Zhou and Z. L. Wang. Springer

BARBIERI MARCO
(syllabus)
see the professor's profile
(reference books)
see the professor's profile

6  FIS/03  32    28    Core compulsory activities  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  

20402215 
EXPERIMENTAL METHODS IN CONDENSED MATTER PHYSICS
(objectives)
Provide the student with the theoretical and methodological bases of fundamental spectroscopies for the characterization of the physical properties of matter in the various aggregation phases

RUOCCO ALESSANDRO
(syllabus)
Basic concepts and potential scattering in atomic collision.
(reference books)
Electronatom collision. Scattering from surfaces. Energy loss spectroscopy. Dielectric theory. Resonant Channels, Fano profiles. Photoemission and photoabsorption spectroscopies. Phenomenology of photoemission and photoabsorption experiments. The Koopmans theorem, satellite peaks, Chemical shift. Photemission from solids, the threestep model. Angle resolved photoemission, photoelectron diffraction. Exafs and Nexafs. BJ B.H. Bransden, C.J. Joachain “Physics of Atoms and Molecules”, Longman Scientific and Technical, John Whiley and sons
CM C.M. Bertoni, Radiationmatter interaction: absorption, photoemission, scattering , in: “Synchrotron radiation: fundamentals, methodologies and applications”, S. Mobilio and G. Vlaic Eds.. SIF, Bologna (2003) Lu H. Luth, “Surface and interface of solid materials”, Springer study edition, 1995 Hu S. Hufner, “Photoelectron spectroscopy”, Solid State Sciences Vol. 82, Springer, 1995 SM S. Mobilio, Interaction between radiation and matter: an introduction, in: “Synchrotron radiation: fundamentals, methodologies and applications”, S. Mobilio and G. Vlaic Eds.. SIF, Bologna (2003) 
9  FIS/03  48  36      Related or supplementary learning activities  ITA  



Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  



20402228 
TRAINING
(objectives)
The internship / stage activity is a work that the student carries out under the guidance of a lecturer both in the university field, and in external sites affiliated with the University; provides the student with the ability to synthesize the acquired global knowledge, applying it to the drafting and elaboration of the thesis work

6          Other activities  ITA  
20410392 
Lingua inglese
(objectives)
Level B2 provides the student with a more indepth ability to communicate the conclusions, as well as the knowledge underlying them, of what has been learned, clearly and critically, also through the use in written and oral form of the English language and disciplinary lexicons, if necessary using the IT tools necessary for the presentation, acquisition and exchange of scientific data also through written documents, diagrams and diagrams. Ability to support a scientific discussion using the topics learned.

4  40        Other activities  ITA  
20401594 
FINAL EXAM
(objectives)
Demonstration by the student of the ability to deal with specific scientific problems, research and / or application of the concepts learned in the various disciplines of Physics

30          Final examination and foreign language test  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language 

20410581 
EXPERIMENTAL PHYSICS OF FUNDAMENTAL INTERACTIONS
(objectives)
The course provides the notions of experimental physics of elementary particles.
The course deals with both experimental and theoretical topics whose aim is to allow students to understand the experimental and theoretical path that led to the formulation of the Standard Model of fundamental interactions as we know it today. The fundamental experiments and discoveries starting from the discovery of elementary particles in cosmic rays up to the production of the vector bosons W and Z and of the Higgs boson are illustrated in detail. At the end of the course the student will have a broad view of particle physics from an experimental point of view, and sufficient knowledge of the theoretical tools necessary to understand its mechanisms. The course is supported by an exercise section whose aim is to reinforce the level of understanding of the topics covered and the calculation methods of the elementary processes, as well as allow students to apply the techniques learned for the calculation of some processes and the relationships between they exist. The course is aimed at all students and those who undertake a path of elementary particle physics that not, providing the basics of physics of elementary particles

Derived from
20410581 FISICA SPERIMENTALE DELLE INTERAZIONI FONDAMENTALI in Fisica LM17 DI MICCO BIAGIO, ORESTANO DOMIZIA
(syllabus)
Program:
(reference books)
1. Principles of invariance and conservation laws. 2. discrete and continuous symmetries; 3. relativistic equations: KleinGordon, Dirac 4. negative energy solutions, helicity, spin, solutions for zero mass, neutrinos 5. relativistic perturbation theory, interaction Hamiltonian, Feynman graphs, propagator as a Green function; 6. Lorentz transformations, laboratory and center of mass system, invariant mass, reaction kinematics, reaction threshold; 7. fields of interaction, Yukawa model; 8. primary and secondary cosmic rays, the muon: decay, mass and average life; 9. kinematics of decays, combination of angular moments, ClebschGordan coefficients, symmetry of the isospin; 10. decay widths and comparison between matrix elements, laws of storage; 11. phase spaction density, Scattering cross section, flux, factor of the space and of the invariant phases, scattering matrix elements; 12. the pion: charge, spin, parity, charge conjugation, isospin; 13. strange particles, hyperons, interaction of the K mesons; 14: strange baryons, mesonic and baryonic octets, SU (3) symmetry, hypercharge, Young's diagrams; 15: discovery of the antiproton, the antibaryons, the Delta resonance; 16: hadronic and mesonic resonances, model at Quarks; 17: representation of the mesons in the quarks model 18: potential scattering, solution of the Schroedingher equation for waves spherical; 19: diffusion and absorption cross section, unitarity limit, optical theorem; 20: resonant cross section, BreitWigner formula, baryon masses with GellMan Okubo formula; 21: the color quantum number, SU (3) representations of color, relationships between spin and SU (3) multiplets; 22: weak interaction, parity violation, madame Wu experiment; 23: oscillation of the K mesons, the Cabibbo angle, the GIM mechanism; 23: discovery of the charm and beauty quarks; 24: decay of D and B mesons, Feynman diagrams, isospin relations; 25: neutrino beams, neutrino flavor, discovery of the neutrino tau; 25: the accelerating machines e + e, hadronic impact section, the ratio R and the number of quarks and colors; 26: measurement of the helicity of the neutrino, discovery of the antineutrino; 27: deep inelastic scattering, parton distribution functions; 27: hadronic colliders, protonantiproton and protonproton: discovery of the W and Z bosons; 28: the Higgs boson 1. course notes, available on the course website;
2. F. Halzen, A. D. Martin, "An Introductory Course in Modern Particle Physics" 3. D. Scroeder, M. Peskin, "An Introduction to Quantum Field Theory" 4. S. Weinberg, "The Quantum Theory of Fields" 
8  FIS/01  64  16      Core compulsory activities  ITA 
20401904 
THEORETICAL PHYSICS I
(objectives)
To study classical electrodynamics in detail, to provide the elements of relativistic quantum mechanics. Provide the basics of field theory and QED

Derived from
20401904 FISICA TEORICA I in Fisica LM17 N0 DEGRASSI GIUSEPPE, Sanfilippo Francesco
(syllabus)
Special Relativity and Electromagnetism.
(reference books)
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and controvariant vectors, tensors, transformation law of the fields. Relativistic Dynamics: fourvelocity, fourmomentum, Minkowski force. Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields, electromagnetic field tensor, covariant formulation of the Maxwell equations, fourpotential, gauge invariance. Conservation laws: Maxwell stress tensor, energymomentum tensor, conservation of energy, momentum and angular momentum. Solution of the Maxwell equations for the fourpotential in the vacuum in the Lorentz gauge. Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect. Cerenkov effect. Relativistic Quantum Mechanics KleinGordon equation. Dirac equation, nonrelativistic limit. Covariance of the Dirac equation. Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality. Quantum Field Theory Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators. Heisenberg representation. Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization. Electromagnetic field, covariant quantization. Global and local invariance. Interaction picture. Smatrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields. Quantzation of the electromagnetic field. Feynman diagrams and rules in QED. Treelevel processes: e+e  mu+ mu, scattering by an external field. V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons. 
8  FIS/02  46  22      Core compulsory activities  ITA 
20402210 
CONDENSED MATTER PHYSICS
(objectives)
The course aims to apply the methods of mechanics quantum to the description of the fundamental properties of solid matter

Derived from
20402210 FISICA DELLA MATERIA CONDENSATA in Fisica LM17 N0 GALLO PAOLA, LUPI LAURA
(syllabus)
Overview on condensed matter. Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: xrays, electrons and neutrons. Quasicrystals. Classification of crystalline solids and bonds. Adiabatic approximation (BornOpenheimer). Lattice vibrational dynamics, phonons. Specific heats of Einstein, Debye and electronic. Electrons in periodic potentials: the Bloch theorem. Theory of the free electron in metals. The many electrons Hamiltonian and one electron approximations: Hartree and Hartree Fock equation. Band theory in crystals: Tight Binding method and the nearly free electron approximation. Electronic properties of relevant crystals. Transport in metals. Intrinsic and doped semiconductors and transport. pn junction. Superconductivity.
(reference books)
Giuseppe Grosso and Giuseppe Pastori Parravicini Solid State Physics Academic Press
others: Neil W. Ashcroft N. David Mermin Solid State Physics Saunders College Charles Kittel Introduzione alla Fisica Dello Stato Solido Casa Editrice Ambrosiana WRITTEN NOTES, PRESENTATIONS AND EXERCISES will be published on the course web site http://webusers.fis.uniroma3.it/~gallop/ 
8  FIS/03  60  20      Core compulsory activities  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  

20402211 
COMPLEMENTS OF MATHEMATICAL METHODS FOR PHYSICS
(objectives)
The aim of the course is to learn the basic tools to deal with Lie algebras and their representations and to acquire computer calculation techniques,both for symbolic and for numerical calculations. Topics of the course
will be dealt with using either Wolfram Language and Python or alternative computer languages preferred by the student.

Derived from
20402211 COMPLEMENTI DI METODI MATEMATICI DELLA FISICA in Fisica LM17 N0 FRANCESCHINI ROBERTO
(syllabus)
Group Theory (CA)
(reference books)
SU(2) and SU(3) The Killing Form Simple Lie Algebras Representations Simple Roots and the Cartan Matrix The Classical Lie Algebras The Exceptional Lie Algebras Casimir Operators and Freudenthal’s Formula The Weyl Group Weyl’s Dimension Formula Reducing Product Representations Subalgebras Branching Rules Numerical Methods Refresh on Probability and Random variables Refresh on Measurement, uncertainty and its propagation Refresh on Curvefitting, leastsquares, optimization Classical numerical integration, speed of convergence Integration MC (Mean, variance) Sampling Strategies Applications Propagation of uncertainties Generation according to a distribution Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html Robert Cahn  SemiSimple Lie Algebras and Their Representations  Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S.  Introduction to Monte Carlo methods arXiv:hepph/0006269 Taylor, J.  An introduction to error analysis  University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre Dubi, A.  Monte Carlo applications in systems engineering  Wiley Disponibile nella biblioteca Scientifica di Roma Tre readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html 
6  FIS/02  34  18      Core compulsory activities  ITA  
20402217 
ELEMENTARY PARTICLE PHYSICS (MOD. A+B)
(objectives)
module A: acquiring the fundamental knowledge on the phenomenological bases of the Standard Model of Elementary Particles and on the principles of particle detection module
B: acquiring indepth knowledge of modern data detection and analysis techniques and the current phenomenological framework in the various sectors of Elementary Particle Physics with and without accelerators 

204022172 
FISICA DELLE PARTICELLE ELEMENTARI  MOD. B
(objectives)
module B: acquiring indepth knowledge of modern techniques for revealing and analyzing data and the current phenomenological framework in the different sectors of Physics of Elementary Particles with and without accelerators

SALAMANNA GIUSEPPE
(syllabus)
SECTION B
(reference books)
 Elements of statistical analysis applied to particle physics experiments  Experiments and results at LEP  Higgs boson searches and mentions of BSM searches at colliders  Examples of experimental neutrino physics and Dark Matter searches  bjet identification and top quark measurements  Complex detectors: magnetic spectrometers, particle identification, large detectors  Scintillators and optical devices (PMT, APD, SiPM). Solid state detectors. Multiwire proportional chambers.  E.m. and hadronic calorimetry  Trigger systems and menucs at modern experiments  ROOT analysis software tutorial TEXTS:
(Leo W.R.)Techniques for Nuclear and Particle Physics Experiments [SpringerVerlag 1994] (Perkins D.H.)Introduction to High Energy Physics, 4th edition, [Cambridge University Press, 2000] (Cahn R.N. and Goldhaber G.)The experimental Foundations of Particle Physics [Cambridge University Press, 1989] (Halzen F., Martin A.D.) Quarks and leptons [Wiley] Additional slides and papers will be uploaded on the Course web page

PETRUCCI FABRIZIO
(syllabus)
SECTION B
(reference books)
 Elements of statistical analysis applied to particle physics experiments  Experiments and results at LEP  Higgs boson searches and mentions of BSM searches at colliders  Examples of experimental neutrino physics and Dark Matter searches  bjet identification and top quark measurements  Complex detectors: magnetic spectrometers, particle identification, large detectors  Scintillators and optical devices (PMT, APD, SiPM). Solid state detectors. Multiwire proportional chambers.  E.m. and hadronic calorimetry  Trigger systems and menucs at modern experiments  ROOT analysis software tutorial TEXTS:
(Leo W.R.)Techniques for Nuclear and Particle Physics Experiments [SpringerVerlag 1994] (Perkins D.H.)Introduction to High Energy Physics, 4th edition, [Cambridge University Press, 2000] (Cahn R.N. and Goldhaber G.)The experimental Foundations of Particle Physics [Cambridge University Press, 1989] (Halzen F., Martin A.D.) Quarks and leptons [Wiley] Additional slides and papers will be uploaded on the Course web page 
6  FIS/04  48        Core compulsory activities  ITA  
204022171 
FISICA DELLE PARTICELLE ELEMENTARI MOD. A
(objectives)
module A: acquiring the fundamental knowledge on the phenomenological bases of the Standard Model of Elementary Particles and on the principles of particle detection

SALAMANNA GIUSEPPE
(syllabus)
SECTION A
(reference books)
a) intro and formal tools:  Relativistic equations, selection rules, cross sections and resonances  Invariance principles and conservation rules, continuous and discrete transformations, Parity, Charge conjugation, Time inversion b) early phenomenology, hadrons:  Strong isospin, Strangeness. Pion isospin and its expt. determination  Dalitz plots and their interpretation. Thetatau puzzle.  Quark model, mentions  Parton model, quark and antiquark density c) Electroweak interactions, decays, flavour mixing  Hamiltonian and phenomenology of weak interazions. Experimental constraints from Wu (P violation) and Goldhaber (neutrino helicity)  Cabibbo angle, GIM mechanism. Discovery of the charm quark and tau lepton. The 1974 "November revolution"  Standard model of electroweak interactions and their experimental confirmations: discovery of neutral currents, Gargamelle expt. W and Z bosons discovery and UA1,2  CP violation, meson mixing. Mentions to Bfactories and measurement of CKM angles from B mesons  Evolution of events at hadronic colliders, parton shower, jet alorithms and related measurements  Neutrino physics from the Fermi theory to the current day: particularly neutrino oscillations d) QCD: anatomy and at work at modern colliders:  QCD, colour, gluons, confinement, DIS  Evolution of events at hadron colliders, parton showers, algorithms, measurements with jets at Tevatron. e) Intro to experimental tools, also useful for theorists  Radiation  matter interactions. Basics of particle detection techniques TEXTS:
(Leo W.R.)Techniques for Nuclear and Particle Physics Experiments [SpringerVerlag 1994] (Perkins D.H.)Introduction to High Energy Physics, 4th edition, [Cambridge University Press, 2000] (Cahn R.N. and Goldhaber G.)The experimental Foundations of Particle Physics [Cambridge University Press, 1989] (Halzen F., Martin A.D.) Quarks and leptons [Wiley] Additional slides and papers will be uploaded on the Course web page

PETRUCCI FABRIZIO
(syllabus)
SECTION A
(reference books)
a) intro and formal tools:  Relativistic equations, selection rules, cross sections and resonances  Invariance principles and conservation rules, continuous and discrete transformations, Parity, Charge conjugation, Time inversion b) early phenomenology, hadrons:  Strong isospin, Strangeness. Pion isospin and its expt. determination  Dalitz plots and their interpretation. Thetatau puzzle.  Quark model, mentions  Parton model, quark and antiquark density c) Electroweak interactions, decays, flavour mixing  Hamiltonian and phenomenology of weak interazions. Experimental constraints from Wu (P violation) and Goldhaber (neutrino helicity)  Cabibbo angle, GIM mechanism. Discovery of the charm quark and tau lepton. The 1974 "November revolution"  Standard model of electroweak interactions and their experimental confirmations: discovery of neutral currents, Gargamelle expt. W and Z bosons discovery and UA1,2  CP violation, meson mixing. Mentions to Bfactories and measurement of CKM angles from B mesons  Evolution of events at hadronic colliders, parton shower, jet alorithms and related measurements  Neutrino physics from the Fermi theory to the current day: particularly neutrino oscillations d) QCD: anatomy and at work at modern colliders:  QCD, colour, gluons, confinement, DIS  Evolution of events at hadron colliders, parton showers, algorithms, measurements with jets at Tevatron. e) Intro to experimental tools, also useful for theorists  Radiation  matter interactions. Basics of particle detection techniques TEXTS:
(Leo W.R.)Techniques for Nuclear and Particle Physics Experiments [SpringerVerlag 1994] (Perkins D.H.)Introduction to High Energy Physics, 4th edition, [Cambridge University Press, 2000] (Cahn R.N. and Goldhaber G.)The experimental Foundations of Particle Physics [Cambridge University Press, 1989] (Halzen F., Martin A.D.) Quarks and leptons [Wiley] Additional slides and papers will be uploaded on the Course web page 
6  FIS/04  48        Core compulsory activities  ITA  
20402218 
THEORETICAL PHYSICS II
(objectives)
Provide the fundamental notions about radiative corrections in QED or nontree processes, about normalization and about the electroweak Standard Model. To acquire skills on the phenomenology of subnuclear physics at the energies of current collectors (LHC).

Derived from
20402218 FISICA TEORICA II in Fisica LM17 N0 MELONI DAVIDE, Giarnetti Alessio
(syllabus)
Feynman diagrams. Treelevel processes. Discrete symmetry
(reference books)
Feynman diagrams and crosssections. Bhabha and Compton scattering. Gauge invariance. Chiral and Majorana representations for the matrices. Parity, charge conjugation and timereversal. Radiative Corrections Divergent behavior of an integral. Primitively divergent diagrams. PauliVillars regularization. Coupling, mass and wavefunction renormalization in a scalar theory. QED. Ward identity. Dimensional regularization. Vacuum polarization and Lamb shift. Running of the coupling constant. Bremsstrahlung, infrared divergencies and their cancellation between real and virtual contributions. Non Abelian Gauge Theories YangMills Lagrangian. QCD. Non Abelian gauge invariance. Running of the strong coupling. Asymtotic freedom. Weak Interactions. Fermi and IVB theories. W propagator. mu decay. Standard Model Lagrangian. Weak angle. Spontaneous symmetry breaking and Higgs mechanism. Mass of the intermediate vector bosons. CKM matrix F. Mandl, G. Shaw: Quantum Field Theory, ed. John Wiley & Sons;
M. Peskin, D. Shroeder: An Introduction to Quantum Field Theory, ed. Frontiers in Physics 
6  FIS/02  34  18      Related or supplementary learning activities  ITA  

Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  

20401859 
SUBNUCLEAR PHYSICS LABORATORY
(objectives)
We provide the skills for the realization of a nuclear or subnuclear physics experiment, gaining experience in group work, with planning, measurement, acquisition and computerized management of data, data analysis, results and final scientific report

MARI STEFANO MARIA
(syllabus)
PROGRAM OF LESSONS IN THE CLASSROOM (EQUIVALENT TO APPROXIMATELY 3 CFU) INTRODUCTORY NOTES ON PARTICLE DETECTORS  PHYSICS OF THE DETECTORS USED IN THE LABORATORY ACTIVITY
(reference books)
(PLASTIC SPARKLERS, LIQUID SPARKLERS, DETECTORS A GAS, ...)  NOTES ON ELECTRONIC DEVICES REQUIRED FOR READING THE DETECTORS, FOR THE TRIGGER AND IL SYSTEM DATA ACQUISITION SYSTEM  CALLS TO PROGRAMMING  STATISTICAL CALLS FOR THE ANALYSIS DATA. PROGRAM OF THE ACTIVITY IN THE LABORATORY (EQUIVALENT A ABOUT 5 CFU) • ESTIMATE OF THE RESPONSE OF THE DETECTORS USED  VERIFICATION OF THE MEASURED SIGNAL  SETTING OF THE DETECTORS • SET UP OF THE APPARATUS  TRIGGER TRAINING • SET UP OF THE DATA ACQUISITION AND DEVELOPMENT SYSTEM OF ANALYSIS SOFTWARE • MEASUREMENT OF THE PROPOSED GREATNESS (VITA MEDIA DEL MESONE MU AND RELATED QUANTITIES, SPECTRUM OF THE ELECTRON OF THE DECAY OF THE MU, SPECTRUM OF HARD COSMIC RAYS, ...) THE STUDENT IS CALLED TO PERFORM A PART ONLY OF THE EXPERIMENTAL ACTIVITY PROPOSED SO THAT IT MAY COMPARE DIRECTLY WITH THE ISSUES OF LABORATORY. THE FINAL MEASURE WILL BE CARRIED OUT IN THE GROUP TESTI CONSIGLIATI:
W.R. Leo  Techniques for Nuclear and Particle Physics Experiment  SpringerVerlag W. Blum, L. Roland  Particle Detection with Drift Chambers  SpringerVerlag T. Ferbel  Experimental Techniques in HighEnergy Nuclear and Particle Physics F. Sauli  Principles of operation of multiwire proportional and drift chambers I. Lombardo  Problemi di fisica nucleare e subnucleare  Zanichelli

DI MICCO BIAGIO
(syllabus)
PROGRAM OF LESSONS IN THE CLASSROOM
(reference books)
INTRODUCTORY NOTES ON PARTICLE DETECTORS  PHYSICS OF THE DETECTORS USED IN THE LABORATORY ACTIVITY (PLASTIC SPARKLERS, LIQUID SPARKLERS, DETECTORS A GAS, ...)  NOTES ON ELECTRONIC DEVICES REQUIRED FOR READING THE DETECTORS, FOR THE TRIGGER AND IL SYSTEM DATA ACQUISITION SYSTEM  CALLS TO PROGRAMMING  STATISTICAL CALLS FOR THE ANALYSIS DATA. PROGRAM OF THE ACTIVITY IN THE LABORATORY (EQUIVALENT A ABOUT 5 CFU) • ESTIMATE OF THE RESPONSE OF THE DETECTORS USED  VERIFICATION OF THE MEASURED SIGNAL  SETTING OF THE DETECTORS • SET UP OF THE APPARATUS  TRIGGER TRAINING • SET UP OF THE DATA ACQUISITION AND DEVELOPMENT SYSTEM OF ANALYSIS SOFTWARE • MEASUREMENT OF THE PROPOSED GREATNESS (VITA MEDIA DEL MESONE MU AND RELATED QUANTITIES, SPECTRUM OF THE ELECTRON OF THE DECAY OF THE MU, SPECTRUM OF HARD COSMIC RAYS, ...) THE STUDENT IS CALLED TO PERFORM A PART ONLY OF THE EXPERIMENTAL ACTIVITY PROPOSED SO THAT IT MAY COMPARE DIRECTLY WITH THE ISSUES OF LABORATORY. THE FINAL MEASURE WILL BE CARRIED OUT IN THE GROUP TESTI CONSIGLIATI:
W.R. Leo  Techniques for Nuclear and Particle Physics Experiment  SpringerVerlag W. Blum, L. Roland  Particle Detection with Drift Chambers  SpringerVerlag T. Ferbel  Experimental Techniques in HighEnergy Nuclear and Particle Physics F. Sauli  Principles of operation of multiwire proportional and drift chambers 

ITA  

Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  



20402228 
TRAINING
(objectives)
The internship / stage activity is a work that the student carries out under the guidance of a lecturer both in the university field, and in external sites affiliated with the University; provides the student with the ability to synthesize the acquired global knowledge, applying it to the drafting and elaboration of the thesis work

6          Other activities  ITA  
20410392 
Lingua inglese
(objectives)
Level B2 provides the student with a more indepth ability to communicate the conclusions, as well as the knowledge underlying them, of what has been learned, clearly and critically, also through the use in written and oral form of the English language and disciplinary lexicons, if necessary using the IT tools necessary for the presentation, acquisition and exchange of scientific data also through written documents, diagrams and diagrams. Ability to support a scientific discussion using the topics learned.

4  40        Other activities  ITA  
20401594 
FINAL EXAM
(objectives)
Demonstration by the student of the ability to deal with specific scientific problems, research and / or application of the concepts learned in the various disciplines of Physics

30          Final examination and foreign language test  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language 

20410581 
EXPERIMENTAL PHYSICS OF FUNDAMENTAL INTERACTIONS
(objectives)
The course provides the notions of experimental physics of elementary particles.
The course deals with both experimental and theoretical topics whose aim is to allow students to understand the experimental and theoretical path that led to the formulation of the Standard Model of fundamental interactions as we know it today. The fundamental experiments and discoveries starting from the discovery of elementary particles in cosmic rays up to the production of the vector bosons W and Z and of the Higgs boson are illustrated in detail. At the end of the course the student will have a broad view of particle physics from an experimental point of view, and sufficient knowledge of the theoretical tools necessary to understand its mechanisms. The course is supported by an exercise section whose aim is to reinforce the level of understanding of the topics covered and the calculation methods of the elementary processes, as well as allow students to apply the techniques learned for the calculation of some processes and the relationships between they exist. The course is aimed at all students and those who undertake a path of elementary particle physics that not, providing the basics of physics of elementary particles

Derived from
20410581 FISICA SPERIMENTALE DELLE INTERAZIONI FONDAMENTALI in Fisica LM17 DI MICCO BIAGIO, ORESTANO DOMIZIA
(syllabus)
Program:
(reference books)
1. Principles of invariance and conservation laws. 2. discrete and continuous symmetries; 3. relativistic equations: KleinGordon, Dirac 4. negative energy solutions, helicity, spin, solutions for zero mass, neutrinos 5. relativistic perturbation theory, interaction Hamiltonian, Feynman graphs, propagator as a Green function; 6. Lorentz transformations, laboratory and center of mass system, invariant mass, reaction kinematics, reaction threshold; 7. fields of interaction, Yukawa model; 8. primary and secondary cosmic rays, the muon: decay, mass and average life; 9. kinematics of decays, combination of angular moments, ClebschGordan coefficients, symmetry of the isospin; 10. decay widths and comparison between matrix elements, laws of storage; 11. phase spaction density, Scattering cross section, flux, factor of the space and of the invariant phases, scattering matrix elements; 12. the pion: charge, spin, parity, charge conjugation, isospin; 13. strange particles, hyperons, interaction of the K mesons; 14: strange baryons, mesonic and baryonic octets, SU (3) symmetry, hypercharge, Young's diagrams; 15: discovery of the antiproton, the antibaryons, the Delta resonance; 16: hadronic and mesonic resonances, model at Quarks; 17: representation of the mesons in the quarks model 18: potential scattering, solution of the Schroedingher equation for waves spherical; 19: diffusion and absorption cross section, unitarity limit, optical theorem; 20: resonant cross section, BreitWigner formula, baryon masses with GellMan Okubo formula; 21: the color quantum number, SU (3) representations of color, relationships between spin and SU (3) multiplets; 22: weak interaction, parity violation, madame Wu experiment; 23: oscillation of the K mesons, the Cabibbo angle, the GIM mechanism; 23: discovery of the charm and beauty quarks; 24: decay of D and B mesons, Feynman diagrams, isospin relations; 25: neutrino beams, neutrino flavor, discovery of the neutrino tau; 25: the accelerating machines e + e, hadronic impact section, the ratio R and the number of quarks and colors; 26: measurement of the helicity of the neutrino, discovery of the antineutrino; 27: deep inelastic scattering, parton distribution functions; 27: hadronic colliders, protonantiproton and protonproton: discovery of the W and Z bosons; 28: the Higgs boson 1. course notes, available on the course website;
2. F. Halzen, A. D. Martin, "An Introductory Course in Modern Particle Physics" 3. D. Scroeder, M. Peskin, "An Introduction to Quantum Field Theory" 4. S. Weinberg, "The Quantum Theory of Fields" 
8  FIS/01  64  16      Core compulsory activities  ITA 
20401904 
THEORETICAL PHYSICS I
(objectives)
To study classical electrodynamics in detail, to provide the elements of relativistic quantum mechanics. Provide the basics of field theory and QED

Derived from
20401904 FISICA TEORICA I in Fisica LM17 N0 DEGRASSI GIUSEPPE, Sanfilippo Francesco
(syllabus)
Special Relativity and Electromagnetism.
(reference books)
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and controvariant vectors, tensors, transformation law of the fields. Relativistic Dynamics: fourvelocity, fourmomentum, Minkowski force. Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields, electromagnetic field tensor, covariant formulation of the Maxwell equations, fourpotential, gauge invariance. Conservation laws: Maxwell stress tensor, energymomentum tensor, conservation of energy, momentum and angular momentum. Solution of the Maxwell equations for the fourpotential in the vacuum in the Lorentz gauge. Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect. Cerenkov effect. Relativistic Quantum Mechanics KleinGordon equation. Dirac equation, nonrelativistic limit. Covariance of the Dirac equation. Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality. Quantum Field Theory Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators. Heisenberg representation. Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization. Electromagnetic field, covariant quantization. Global and local invariance. Interaction picture. Smatrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields. Quantzation of the electromagnetic field. Feynman diagrams and rules in QED. Treelevel processes: e+e  mu+ mu, scattering by an external field. V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons. 
8  FIS/02  46  22      Core compulsory activities  ITA 
20402210 
CONDENSED MATTER PHYSICS
(objectives)
The course aims to apply the methods of mechanics quantum to the description of the fundamental properties of solid matter

Derived from
20402210 FISICA DELLA MATERIA CONDENSATA in Fisica LM17 N0 GALLO PAOLA, LUPI LAURA
(syllabus)
Overview on condensed matter. Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: xrays, electrons and neutrons. Quasicrystals. Classification of crystalline solids and bonds. Adiabatic approximation (BornOpenheimer). Lattice vibrational dynamics, phonons. Specific heats of Einstein, Debye and electronic. Electrons in periodic potentials: the Bloch theorem. Theory of the free electron in metals. The many electrons Hamiltonian and one electron approximations: Hartree and Hartree Fock equation. Band theory in crystals: Tight Binding method and the nearly free electron approximation. Electronic properties of relevant crystals. Transport in metals. Intrinsic and doped semiconductors and transport. pn junction. Superconductivity.
(reference books)
Giuseppe Grosso and Giuseppe Pastori Parravicini Solid State Physics Academic Press
others: Neil W. Ashcroft N. David Mermin Solid State Physics Saunders College Charles Kittel Introduzione alla Fisica Dello Stato Solido Casa Editrice Ambrosiana WRITTEN NOTES, PRESENTATIONS AND EXERCISES will be published on the course web site http://webusers.fis.uniroma3.it/~gallop/ 
8  FIS/03  60  20      Core compulsory activities  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  

20402211 
COMPLEMENTS OF MATHEMATICAL METHODS FOR PHYSICS
(objectives)
The aim of the course is to learn the basic tools to deal with Lie algebras and their representations and to acquire computer calculation techniques,both for symbolic and for numerical calculations. Topics of the course
will be dealt with using either Wolfram Language and Python or alternative computer languages preferred by the student.

Derived from
20402211 COMPLEMENTI DI METODI MATEMATICI DELLA FISICA in Fisica LM17 N0 FRANCESCHINI ROBERTO
(syllabus)
Group Theory (CA)
(reference books)
SU(2) and SU(3) The Killing Form Simple Lie Algebras Representations Simple Roots and the Cartan Matrix The Classical Lie Algebras The Exceptional Lie Algebras Casimir Operators and Freudenthal’s Formula The Weyl Group Weyl’s Dimension Formula Reducing Product Representations Subalgebras Branching Rules Numerical Methods Refresh on Probability and Random variables Refresh on Measurement, uncertainty and its propagation Refresh on Curvefitting, leastsquares, optimization Classical numerical integration, speed of convergence Integration MC (Mean, variance) Sampling Strategies Applications Propagation of uncertainties Generation according to a distribution Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html Robert Cahn  SemiSimple Lie Algebras and Their Representations  Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S.  Introduction to Monte Carlo methods arXiv:hepph/0006269 Taylor, J.  An introduction to error analysis  University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre Dubi, A.  Monte Carlo applications in systems engineering  Wiley Disponibile nella biblioteca Scientifica di Roma Tre readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html 
6  FIS/02  34  18      Core compulsory activities  ITA  
20402218 
THEORETICAL PHYSICS II
(objectives)
Provide the fundamental notions about radiative corrections in QED or nontree processes, about normalization and about the electroweak Standard Model. To acquire skills on the phenomenology of subnuclear physics at the energies of current collectors (LHC).

MELONI DAVIDE
(syllabus)
Feynman diagrams. Treelevel processes. Discrete symmetry
(reference books)
Feynman diagrams and crosssections. Bhabha and Compton scattering. Gauge invariance. Chiral and Majorana representations for the matrices. Parity, charge conjugation and timereversal. Radiative Corrections Divergent behavior of an integral. Primitively divergent diagrams. PauliVillars regularization. Coupling, mass and wavefunction renormalization in a scalar theory. QED. Ward identity. Dimensional regularization. Vacuum polarization and Lamb shift. Running of the coupling constant. Bremsstrahlung, infrared divergencies and their cancellation between real and virtual contributions. Non Abelian Gauge Theories YangMills Lagrangian. QCD. Non Abelian gauge invariance. Running of the strong coupling. Asymtotic freedom. Weak Interactions. Fermi and IVB theories. W propagator. mu decay. Standard Model Lagrangian. Weak angle. Spontaneous symmetry breaking and Higgs mechanism. Mass of the intermediate vector bosons. CKM matrix F. Mandl, G. Shaw: Quantum Field Theory, ed. John Wiley & Sons;
M. Peskin, D. Shroeder: An Introduction to Quantum Field Theory, ed. Frontiers in Physics

Giarnetti Alessio
(syllabus)
see profile of the teacher holding the course
(reference books)
see profile of the teacher holding the course

6  FIS/02  34  18      Core compulsory activities  ITA  
20402219 
ELEMENTARY PARTICLE PHYSICS (MOD. A)
(objectives)
To acquire the fundamental knowledge on the phenomenological bases of the Standard Model of Elementary Particles and on the principles of particle detection

6  FIS/04  48        Core compulsory activities  ITA  
20410086 
ELEMENTI DI RELATIVITA' GENERALE, ASTROFISICA E COSMOLOGIA
(objectives)
The course aims to provide students with the basic concepts of general relativity and its applications to physical systems, with particular reference to compact objects (black holes), gravitational waves and the universe

Derived from
20410086 ELEMENTI DI RELATIVITA' GENERALE, ASTROFISICA E COSMOLOGIA in Fisica LM17 BRANCHINI ENZO FRANCO
(syllabus)
 SPECIAL RELATIVITY. VECTORS AND TENSORS. METRIC TENSOR. ENERGYMOMENTUM TENSOR.
(reference books)
 GENERAL RELATIVITY. UNDERLYING CONCEPTS. AFFINE CONNECTION. PARALLEL TRANSPORT. GEODESICS EQUATION.  SYMMETRY AND KILLING VECTORS. RIEMANN TENSOR. SINGULARITY.  EINSTEIN EQUATIONS.  SCHWARZSCHILD METRIC.  ORBITS IN THE SCHWARZSCHILD METRIC. MERCURY’S ORBIT.  NON ROTATING BLACK HOLES. EVENT HORIZON AND THE CHOICE OF COORDINATES.  KERR METRIC. ROTATING BLACK HOLES AND FRAME DRAGGING.  INTRODUCTION TO GRAVITATIONAL WAVES.  THE COSMOLOGICAL PRINCIPLE AND ROBERTSONWALKER METRIC.  FRIEDMAN EQUATIONS. NEWTONIAN LIMIT.  COSMOLOGICAL REDSHIFT. COSMOLOGICAL HORIZONS. COMOVING COORDINATES AND PROPER DISTANCE.  LUMINOSITY DISTANCE. ANGULAR DIAMETER DISTANCE.  OBSERVATIONAL TESTS: HUBBLE TEST, ANGULAR DIAMETER TEST, NUMBER COUNTS.  FLUIDS RELEVANT IN COSMOLOGY: EQUATION OF STATE AND DENSITY EVOLUTION. Cosmological constant.  THE EQUIVALENCE EPOCH.  THERMAL HISTORY OF THE UNIVERSE: DECOUPLING. RECOMBINATION.  MATTER/ANTIMATTER AND THE BARYON ASYMMETRY.  PLANCK EPOCH AND QUANTUM GRAVITY.  HORIZON PARADOX. FLATNESS PARADOX. INFLATIONARY SOLUTION. COSMIC INFLATION.  DARK MATTER.  A BRIEF HISTORY OF THE UNIVERSE. HADRONIC EPOCH. LEPTONIC EPOCH. RADIATIVE EPOCH.  NEUTRINO DECOUPLING.  COSMOLOGICAL NUCLEOSYNTHESIS. MATTER EPOCH. FIRST OBJECTS. REIONIZATION.  INHOMOGENEITY AND ANISOTROPY. JEANS GRAVITATIONAL INSTABILITY AND THE GROWTH OF COSMIC STRUCTURES Carroll S. Spaceitme Geometry [Pearson 2003]
Coles P., Lucchin F. Cosmology [Wiley 2000] Kolb E., Turner M. The eraly Universe [Addison Wesley 1990] 
6  FIS/05  48        Core compulsory activities  ITA  

Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  

20401139 
FUNDAMENTAL INTERACTIONS PHYSICS
(objectives)
To introduce the physics of fundamental interactions in the Standard Model and the formalism of the Field Theory that underlies it.

TARANTINO CECILIA
(syllabus)
Introductive Lectures:
(reference books)
Green Functions, Feynman Diagrams, Exponentiation of disconnected diagrams, IN and OUT states, SMatrix, SMatrix in terms of Feynman diagrams, KaellenLehmann Spectral Representation, LSZ Reduction Formula, Optical Theorem. Renormalization: Superficial Divergence Degree of Diagrams, Renormalized Perturbation Theory, CallanSymanzik Equation, Beta and Gamma Functions, Running coupling, Leading Logarithm Resummation. Path Integral Method: Introduction to Path Integral Formalism, Path Integral for a Field Theory (Path Int.for a scalar field thoery), Green functions in terms of Path Int., Feynman rules from Path Int., Generating Functional, QED Quantization (FaddeevPopov Method), Dirac Field Quantization, Quantization of Nonabelian Gauge Theories, Ghosts. Michael E. Peskin, Daniel V. Schroeder "An Introduction to Quantum Field Theory";
Franz Mandl, Graham Shaw "Quantum Field Theory". 
8  FIS/02  64        Core compulsory activities  ITA  

Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language 

20402258 
RELATIVITY THEORY
(objectives)
(English)
To make the student familiar with the conceptual assumptions of the Theory of General Relativity, both as a geometric theory of spacetime and by emphasizing analogies and differences with field theories based on local symmetries that describe the interactions between elementary particles. Illustrate the essential elements of differential geometry necessary to formalize the proposed concepts. Introduce the student to extensions of the theory of interest for current theoretical research.

FRANCIA DARIO
(syllabus)
Introductory notions
(reference books)
Recap of Special Relativity. Lorentz transformations in Minkowski’s space. Vectors in Minkowski’s space. Basis of the tangent space. Cotangents space and dual vectors in Minkowski’s space. Basis of cotangent space. Lorentz transformations of vectors and dual vectors. Tensors in Minkowski’s space. Properties of vectors, dual vectors and tensors in Minkowski’s space. Definition of symmetric and antisymmetric tensor. Symmetrization and antisymmetrization of a generic tensor. Metric in Minkowski’s space: definition and properties. Operations related to the metric: scalar products, rising and lowering indices of a tensor, contractions and trace of a tensor. Equivalence between inertial and gravitational mass. Weak Equivalence Principle (WEP), Einstein’s equivalence Principle (EEP). Basic notions of differential geometry Introduction to the notion of manifold. Definition and properties of maps. Injective and suriective maps (some examples included). Composition of charts. Invertible charts. Definition of diffeomorphism. Definition of chart (or coordinate system). Definition of atlas. Definition of manifold. Product of manifolds. Formal coordinate independent definition of vector. Demonstration that the dimension of the tangent space coincides with the one of the corresponding manifold. Basis (or coordinate system) of the tangent space. Coordinate transformations. Coordinate transformations of the components of a vector. Definition and properties of the tangent field. Definition of one parameter group of diffeomorphisms. Definition of integral curves. Commutator of two vectors. Coordinate independent definition of dual vector (oneform). Cotangent space and corresponding basis. Coordinate transformation of the components of a oneform. Coordinate independent definition of tensor. Demonstration that the partial derivative of a tensor is not a tensor. Metric: signature and canonical form. Tensor densities. Differential forms. Wedge product. Exterior derivative. Closed and exact form. Poincarre Lemma (statement only). Hodge duality. Maxwell equations expressed in term of exterior derivative and hodge duality (only small reference). Integration over a manifold: volume element in terms of the determinant of the metric. Maps between manifold: pullback and pushforward. Pullback and pushforward associated to diffeomorphisms. Equivalence between diffeomorphisms and coordinate transformations. Vector field associated to diffeomorphisms. Lie Derivative: definition and general properties. Action of Lie’s derivative on scalars, vectors, oneforms and tensors. General Relativity as diffeomorphism invariant theory. Analogy between gauge transformations and diffeomorphisms. Symmetries. Notion of submanifold. Immersed and embedded submanifolds. Notion of hypersurface and boundary of a manifold. Integration on manifolds again: differential form as generic volume element. Orientation and orientable manifold. Covering of the manifold through partition of unity. Integration of pforms over submanifold. Demonstrations that the volume element can be expressed in terms of the determinant of the metric. Stokes theorem (no demonstration). Connection, Covariant Derivative, Curvature Lie’s Algebra and Lie’s group. Action from the right and from the left. Left and rightinvariant vectors. Structure constants. Examples of Lie groups. MaurerCartan forms. MaurerCartan’s equations. Action of Lie Groups on manifolds. Definition of free, effective and transitive action. Orbit and stabilizer. Algebric definition of connection and covariant derivative. General properties of covariant derivatives. Action of coordinate transformations on the connection. Demonstration that the difference of Christoffel coefficients associated to two different connections transforms as a tensor; torsion tensor, torsionfree and metric connection. Demonstrations that for any given metric exists a connection (metric connections) for which the covariant derivative of the metric is zero. Formal construction of the covariant derivative from the notion of parallel transport (qualitative introduction). Fiber bundle. Trivial and locally trivializable bundles. Local trivilizations. Maps between fiber bundles (notions). Defintion of bundle atlas, Gatlas, Gstructure. Fiber Bundle with structure group G. Definition of Principal Bundle. Definition of section of a bundle. Vector bundle and bundle of basis, definition and general properties. Relation between principle bundle, vectorbundle and bundle of frames (definition of associated vector bundle to a principal bundle. Construction of the covariante derivative on a vectorbundle (only the knowledge of the fundamental logical steps is required for the exam). Curvature tensor as 2form on a fiber bundle. Geometrical interpretation of the curvature. Bianchi identity. Fiber metric. Ortogonal basis. Connections and gauge theories: electromagnetism as simple example. Soldering form. Choice of the gauge. Ortonormal and metric gauge. LeviCivita connection; Riemann’s tensor : definition and properties. Ricci’s tensor and scalar, Weyl’s tensor. Globally and locally inertial coordinates. Einstein’s theory of gravity Minimal coupling. Particle in a gravitational field: affine parameter, selfparallel curves. Geodesic’s equations. Geodesic deviation. Derivation of the Einstein’s equations from Newton’s limit. Lagrangian derivations of Einstein’s equations. General considerations on the structure of Einstein’s equations. Choice of the gauge. Energy conditions. Symmetries and Killing vectors: version of Noether’s theorem from general relativity. Maximal number of linearly independent Killing vectors on a manifold. Homogenous and isotropic manifold. Spaces at constant curvature. Metric in spaces at constant curvature. Notable solutions of Einstein’s equations Static spherically symmetric spacetimes. Determination of Schwarzschild’s metric. Cosmological solution. Spatially homogeneous and isotropic spacetime. Frieman’s RobertsonWalker metric. Friedman’s equations. Coordinate singularities. Case of study: Schwarzschild radius. Rindler metric. Kruskal coordinates. Black hole solution. Perturbation around a background metric. Case of study:perturbation of flat metric. Degrees of freedom. Linearized Einstein’s equations. Choice of the gauge. Linearized Einstein’s equations in vacuum: gravitational waves. Solutions in presence of the source (only few words). Advanced concepts Conformal transformations. Cotton’s tensor. Conformally flat metric. Demonstration of the theorem: a metric is conformally flat if and only if Weyl (Cotton) tensor is null. Conformal group. Conformal Killing vectors. Alternative theories of gravity. Scalartensor theories. Jordan and Einstein’s frames. Testi consigliati :
1. S. Carrol Space time and Geometry: An Introduction to General Relativity (Addison Wesley, 2004); 2. R. Wald General Relativity (The Chicago Press, 1984); 3. B. Schutz A First Course in General Relativity (Cambridge Press) 4. B. Schutz Geometrical Methods of Mathematical Physics (Cambridge Press) 5. S. Weinberg Gravitation and Cosmologyprinciples and application of the general theory of relativity (John Weiley & Sons, 1972); 6. people.sissa.it/~percacci/lectures/general/index.html 
6  FIS/02  48        Related or supplementary learning activities  ITA 
20402228 
TRAINING
(objectives)
The internship / stage activity is a work that the student carries out under the guidance of a lecturer both in the university field, and in external sites affiliated with the University; provides the student with the ability to synthesize the acquired global knowledge, applying it to the drafting and elaboration of the thesis work

6          Other activities  ITA  
20410392 
Lingua inglese
(objectives)
Level B2 provides the student with a more indepth ability to communicate the conclusions, as well as the knowledge underlying them, of what has been learned, clearly and critically, also through the use in written and oral form of the English language and disciplinary lexicons, if necessary using the IT tools necessary for the presentation, acquisition and exchange of scientific data also through written documents, diagrams and diagrams. Ability to support a scientific discussion using the topics learned.

4  40        Other activities  ITA  
20401594 
FINAL EXAM
(objectives)
Demonstration by the student of the ability to deal with specific scientific problems, research and / or application of the concepts learned in the various disciplines of Physics

30          Final examination and foreign language test  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language 

20410581 
EXPERIMENTAL PHYSICS OF FUNDAMENTAL INTERACTIONS
(objectives)
The course provides the notions of experimental physics of elementary particles.
The course deals with both experimental and theoretical topics whose aim is to allow students to understand the experimental and theoretical path that led to the formulation of the Standard Model of fundamental interactions as we know it today. The fundamental experiments and discoveries starting from the discovery of elementary particles in cosmic rays up to the production of the vector bosons W and Z and of the Higgs boson are illustrated in detail. At the end of the course the student will have a broad view of particle physics from an experimental point of view, and sufficient knowledge of the theoretical tools necessary to understand its mechanisms. The course is supported by an exercise section whose aim is to reinforce the level of understanding of the topics covered and the calculation methods of the elementary processes, as well as allow students to apply the techniques learned for the calculation of some processes and the relationships between they exist. The course is aimed at all students and those who undertake a path of elementary particle physics that not, providing the basics of physics of elementary particles

Derived from
20410581 FISICA SPERIMENTALE DELLE INTERAZIONI FONDAMENTALI in Fisica LM17 DI MICCO BIAGIO, ORESTANO DOMIZIA
(syllabus)
Program:
(reference books)
1. Principles of invariance and conservation laws. 2. discrete and continuous symmetries; 3. relativistic equations: KleinGordon, Dirac 4. negative energy solutions, helicity, spin, solutions for zero mass, neutrinos 5. relativistic perturbation theory, interaction Hamiltonian, Feynman graphs, propagator as a Green function; 6. Lorentz transformations, laboratory and center of mass system, invariant mass, reaction kinematics, reaction threshold; 7. fields of interaction, Yukawa model; 8. primary and secondary cosmic rays, the muon: decay, mass and average life; 9. kinematics of decays, combination of angular moments, ClebschGordan coefficients, symmetry of the isospin; 10. decay widths and comparison between matrix elements, laws of storage; 11. phase spaction density, Scattering cross section, flux, factor of the space and of the invariant phases, scattering matrix elements; 12. the pion: charge, spin, parity, charge conjugation, isospin; 13. strange particles, hyperons, interaction of the K mesons; 14: strange baryons, mesonic and baryonic octets, SU (3) symmetry, hypercharge, Young's diagrams; 15: discovery of the antiproton, the antibaryons, the Delta resonance; 16: hadronic and mesonic resonances, model at Quarks; 17: representation of the mesons in the quarks model 18: potential scattering, solution of the Schroedingher equation for waves spherical; 19: diffusion and absorption cross section, unitarity limit, optical theorem; 20: resonant cross section, BreitWigner formula, baryon masses with GellMan Okubo formula; 21: the color quantum number, SU (3) representations of color, relationships between spin and SU (3) multiplets; 22: weak interaction, parity violation, madame Wu experiment; 23: oscillation of the K mesons, the Cabibbo angle, the GIM mechanism; 23: discovery of the charm and beauty quarks; 24: decay of D and B mesons, Feynman diagrams, isospin relations; 25: neutrino beams, neutrino flavor, discovery of the neutrino tau; 25: the accelerating machines e + e, hadronic impact section, the ratio R and the number of quarks and colors; 26: measurement of the helicity of the neutrino, discovery of the antineutrino; 27: deep inelastic scattering, parton distribution functions; 27: hadronic colliders, protonantiproton and protonproton: discovery of the W and Z bosons; 28: the Higgs boson 1. course notes, available on the course website;
2. F. Halzen, A. D. Martin, "An Introductory Course in Modern Particle Physics" 3. D. Scroeder, M. Peskin, "An Introduction to Quantum Field Theory" 4. S. Weinberg, "The Quantum Theory of Fields" 
8  FIS/01  64  16      Core compulsory activities  ITA 
20401904 
THEORETICAL PHYSICS I
(objectives)
To study classical electrodynamics in detail, to provide the elements of relativistic quantum mechanics. Provide the basics of field theory and QED

Derived from
20401904 FISICA TEORICA I in Fisica LM17 N0 DEGRASSI GIUSEPPE, Sanfilippo Francesco
(syllabus)
Special Relativity and Electromagnetism.
(reference books)
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and controvariant vectors, tensors, transformation law of the fields. Relativistic Dynamics: fourvelocity, fourmomentum, Minkowski force. Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields, electromagnetic field tensor, covariant formulation of the Maxwell equations, fourpotential, gauge invariance. Conservation laws: Maxwell stress tensor, energymomentum tensor, conservation of energy, momentum and angular momentum. Solution of the Maxwell equations for the fourpotential in the vacuum in the Lorentz gauge. Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect. Cerenkov effect. Relativistic Quantum Mechanics KleinGordon equation. Dirac equation, nonrelativistic limit. Covariance of the Dirac equation. Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality. Quantum Field Theory Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators. Heisenberg representation. Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization. Electromagnetic field, covariant quantization. Global and local invariance. Interaction picture. Smatrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields. Quantzation of the electromagnetic field. Feynman diagrams and rules in QED. Treelevel processes: e+e  mu+ mu, scattering by an external field. V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons. 
8  FIS/02  46  22      Core compulsory activities  ITA 
20402210 
CONDENSED MATTER PHYSICS
(objectives)
The course aims to apply the methods of mechanics quantum to the description of the fundamental properties of solid matter

Derived from
20402210 FISICA DELLA MATERIA CONDENSATA in Fisica LM17 N0 GALLO PAOLA, LUPI LAURA
(syllabus)
Overview on condensed matter. Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: xrays, electrons and neutrons. Quasicrystals. Classification of crystalline solids and bonds. Adiabatic approximation (BornOpenheimer). Lattice vibrational dynamics, phonons. Specific heats of Einstein, Debye and electronic. Electrons in periodic potentials: the Bloch theorem. Theory of the free electron in metals. The many electrons Hamiltonian and one electron approximations: Hartree and Hartree Fock equation. Band theory in crystals: Tight Binding method and the nearly free electron approximation. Electronic properties of relevant crystals. Transport in metals. Intrinsic and doped semiconductors and transport. pn junction. Superconductivity.
(reference books)
Giuseppe Grosso and Giuseppe Pastori Parravicini Solid State Physics Academic Press
others: Neil W. Ashcroft N. David Mermin Solid State Physics Saunders College Charles Kittel Introduzione alla Fisica Dello Stato Solido Casa Editrice Ambrosiana WRITTEN NOTES, PRESENTATIONS AND EXERCISES will be published on the course web site http://webusers.fis.uniroma3.it/~gallop/ 
8  FIS/03  60  20      Core compulsory activities  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  

20402211 
COMPLEMENTS OF MATHEMATICAL METHODS FOR PHYSICS
(objectives)
The aim of the course is to learn the basic tools to deal with Lie algebras and their representations and to acquire computer calculation techniques,both for symbolic and for numerical calculations. Topics of the course
will be dealt with using either Wolfram Language and Python or alternative computer languages preferred by the student.

Derived from
20402211 COMPLEMENTI DI METODI MATEMATICI DELLA FISICA in Fisica LM17 N0 FRANCESCHINI ROBERTO
(syllabus)
Group Theory (CA)
(reference books)
SU(2) and SU(3) The Killing Form Simple Lie Algebras Representations Simple Roots and the Cartan Matrix The Classical Lie Algebras The Exceptional Lie Algebras Casimir Operators and Freudenthal’s Formula The Weyl Group Weyl’s Dimension Formula Reducing Product Representations Subalgebras Branching Rules Numerical Methods Refresh on Probability and Random variables Refresh on Measurement, uncertainty and its propagation Refresh on Curvefitting, leastsquares, optimization Classical numerical integration, speed of convergence Integration MC (Mean, variance) Sampling Strategies Applications Propagation of uncertainties Generation according to a distribution Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html Robert Cahn  SemiSimple Lie Algebras and Their Representations  Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S.  Introduction to Monte Carlo methods arXiv:hepph/0006269 Taylor, J.  An introduction to error analysis  University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre Dubi, A.  Monte Carlo applications in systems engineering  Wiley Disponibile nella biblioteca Scientifica di Roma Tre readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html 
6  FIS/02  34  18      Core compulsory activities  ITA  
20402232 
Quantum Theory of Matter
(objectives)
The course intends to offer an introduction to the methods of field theory applied to the study of manybody systems of Matter Physics, in particular the theoretical study of quantum phenomena that characterize matter at low temperatures such as superfluidity and superconductivity is developed

Derived from
20410022 TEORIA QUANTISTICA DELLA MATERIA MOD. A in Fisica LM17 RAIMONDI ROBERTO
(syllabus)
 Fluctuationdissipation theorem and linear response theory.
(reference books)
Green functions at zero temperature. Lehmann decomposition. Analytical properties.  Perturbative development and Feynman diagrams. Dyson equation.  Green functions at finite temperature: Matsubara technique.  HartreeFock theory and RPA approximation. ThomasFermi screen. Lindhard function. Fermi liquid theory.  Phenomenology of superfluidity. Landau theory. Microscopic theory of superfluidity. Bogolubov theory.  Phenomenology of superconductivity.  Microscopic BCS theory of superconductivity. Gorkov's derivation of the LandauGinzburg equations. Theory of electronic transport in disordered systems. 1 Carlo Di Castro, Roberto Raimondi, Statistical Mechanics and Applications in Condensed Matter, Cambridge University Press 2015.
2 Piers Coleman, Introduction to ManyBody Physics, Cambridge University Press 2015. 
6  FIS/03  60        Core compulsory activities  ITA  
20402221 
COMPLEMENTS OF CONDENSED MATTER PHYSICS
(objectives)
Give the student an indepth understanding of the transport properties of solid systems and their response to electromagnetic fields

Derived from
20410020 COMPLEMENTI DI FISICA DELLA MATERIA CONDENSATA in Fisica LM17 DE SETA MONICA
(syllabus)
Electronic properties of selected crystals
(reference books)
Reminds on band structure calculation methods. Electronic structure of molecular and ionic solids. Band structure of IIVI, IIIV systems and of covalent crystals with diamond structure. Impurity levels in doped semiconductors. Internal energy, pressure and compressibility of an electron gas. Band structures and Fermi surfaces of selected metals. Transport properties: The Drude Model. Semiclassical Equations of transport. Boltzmann equation. Relaxation time approximation. Static and dynamic electrical conductivity in metals. Thermoeletrictic power and thermal conductivity. Transport in homogeneous and doped semiconductors. Drift and diffusion currents. Generation and recombination of electronhole pairs in semiconductors. Continuity equation. Recombination times and diffusion length. Current voltage characteristics of the pn junction. Metalsemiconductor junction. Electron phonon interaction. Matrix elements and selection rules. Optical properties of solids Maxwell Equations in solids. Complex Dielectric Constant. Absorption and reflection coefficients. Kramers Kronig Relations. The Drude theory of the optical properties of metals. Optical properties of semiconductors and insulators. Direct interband transitions and critical points. Optical constants of Ge and Graphite. Absorption from impurity levels. Exciton effects. Indirect phononassisted transitions. Twophoton absorption. Raman Scattering. Optical phonon absorption. Electron gas in magnetic fields Energy levels and density of states of a free electron gas in a magnetic fields. Orbital magnetic susceptibility and Haasvan Alphen effect. Magnetoresistivity and classical Hall effect. Phenomenology of the quantum Hall effect. Magnetic properties of matter. Quantum mechanical treatment of magnetic suscectibility. Pauli paramagnetism. Magnetic suscectibility of closedshell systems. Permanent magnetic dipoles in atoms and ions with partially filled shells. Paramagnetism of localized magnetic moments. Curie and Van Vleck paramagnetism. Magnetic ordering in crystals. Mean field theory of ferromagnetism: Weiss model. CurieWeiss law. Critical temperature. Ferromagnetism, exchange interaction and Heisemberg model. Microscopic origin of the coupling between localized magnetic moments. Dipolar interaction and magnetic domains. AshcroftMermin: "Solid State Physics"
GrossoPastoriParravicini: "Solid State Physics" 
6  FIS/03  48        Related or supplementary learning activities  ITA  
20410584 
COMPLEX NETWORKS
(objectives)
To understand algorithms related to complex systems, writing, executing and optimising simulation programs of such systems (Montecarlo and molecular dynamics programs) and analysing the data produced by simulations.

Derived from
20410571 FS520 – RETI COMPLESSE in Scienze Computazionali LM40 CAMISASCA GAIA
(syllabus)
NETWORKS AND GRAPHS
(reference books)
 Graphs, trees and networks  Centrality measures and degree  Random graphs, the Erdős and Rényi model SMALL WORLDS NETWORKS  Definition of Small World  Clustering Coefficient  The WattsStrogatz model GENERALISED RANDOM GRAPHS  Statistical description of networks  Degree Distributions of real networks  Generalization of the Erdős–Rényi model  Radom graphs with powerlaw degree distributions GROWING GRAPHS  Dynamical evolution of random graphs  The Barabási–Albert model DEGREE CORRELATIONS  Correlated networks  Assortative and Disassortative Networks, "Rich Club" behavior WEIGHTED NETWORKS  Beyond purely topological networks: tuning the interactions in a complex system  The BarratBarthélemyVespignani model INTRODUCTION TO DYNAMICAL PROCESSES: THEORY AND SIMULATION TESTO PRINCIPALE DEL CORSO:
V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Cambridge University press (2017) TESTO UTILIZZATO PER PICCOLE PARTI DI PROGRAMMA: A. Barrat, M. Barthelemy, A. Vespignani, "Dynamical processes on complex networks", Cambridge University Press (2008) Main textbook: 
6  FIS/03  60        Core compulsory activities  ITA  

Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  

20401425 
STATISTICAL MECHANICS
(objectives)
The course aims to give an overview of modern developments in statistical mechanics. In particular, starting from the theory of phase transitions and critical phenomena, we want to show how the concepts underlying the renormalization group method emerged. This method is now widely used in various fields of statistical mechanics. Critical phenomena constitute the classic application of the method, which is illustrated in detail in the first 6 credits of the course. These first 6 credits can therefore be used from multiple addresses.
The remaining 2 credits focus on Monte Carlo methods and molecular dynamics in the study of phase equilibria and rare events with applications in the physics of matter.

LUPI LAURA
(syllabus)
1st module program (6 credits)
(reference books)
Introduction to thermodynamics. Thermodynamic potentials. Phase transitions and Van der Waals equation. Fluctuations and stability. Phase transitions and thermodynamic limit. Microscopic derivation of the Van der Waals equation. Critical point behavior of the Van der Waals equation. CurieWeiss theory of ferromagnetism. Landau theory of second species transitions. Ginzburg criterion for the validity of the middle field theory. The role of symmetry and dimensionality: the MerminWagner theorem. Renormalization team. KadanoffWilson transformation. Calculation of fixed points for the LandauWilson model and development in epsilon. II module program (2 credits) Spin glasses Methods for calculating free energy. Advanced techniques for simulating rare events. Statistical Mechanics and Applications in Condensed Matter
by Carlo Di Castro and Roberto Raimondi Cambridge University Press 2015 ISBN: 9781107039407

LUPI LAURA
(syllabus)
1st module program (6 credits)
(reference books)
Introduction to thermodynamics. Thermodynamic potentials. Phase transitions and Van der Waals equation. Fluctuations and stability. Phase transitions and thermodynamic limit. Microscopic derivation of the Van der Waals equation. Critical point behavior of the Van der Waals equation. CurieWeiss theory of ferromagnetism. Landau theory of second species transitions. Ginzburg criterion for the validity of the middle field theory. The role of symmetry and dimensionality: the MerminWagner theorem. Renormalization team. KadanoffWilson transformation. Calculation of fixed points for the LandauWilson model and development in epsilon. II module program (2 credits) Spin glasses Methods for calculating free energy. Advanced techniques for simulating rare events. Statistical Mechanics and Applications in Condensed Matter
by Carlo Di Castro and Roberto Raimondi Cambridge University Press 2015 ISBN: 9781107039407 
8  FIS/02  80        Core compulsory activities  ITA  
20410585 
PHYSICS OF LIQUIDS AND SOFT MATTER
(objectives)
To offer an introduction to the modern physics of liquids, understood as the study of the phenomenology of fluids starting from interatomic force laws. We will study the theoretical methods based on integral equations that allow us to describe the structure of the liquid. Computer numerical simulation methods applied to the physics of liquids will be introduced. Then we will study the correlation functions and the theory of linear response with applications to the study of the dynamics of liquids in the hydrodynamic limit and in the viscoelastic limit. The memory functions will be introduced. The physics of supercooled liquids and the study of the glass transition will be discussed

GALLO PAOLA
(syllabus)
1  Review of Thermodynamics and Statistical Mechanics.
(reference books)
Extensive and intensive thermodynamic functions. Conditions of equilibrium. Legendre transforms and thermodynamic potentials. Phase stability conditions. Phase transitions and their classification. Van der Waals equation. Review of the theory of statistical ensembles. Fluctuations. 2  Forces between atoms and shortrange order. Characterization of the liquid state of matter. Characterization of soft materials. Forces between atoms and effective potentials. Distribution functions in the canon and the grand canon. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid with Xray and neutron scattering techniques. Structure factors and radial distribution functions of liquid and liquid molecular mixtures. Classic density functional theory. OrnsteinZernike equation. Closing relations for the density functional. 3  Numerical simulation of liquid and soft material Stochastic and deterministic simulation methods. Molecular Dynamics Method. Verletstyle algorithms. Molecular dynamics at constant temperature and pressure. The Monte Carlo simulation method. Monte Carlo simulation in different ensembles. Phase equilibrium simulation methods. Application of Monte Carlo and Molecular Dynamics methods to complex liquids and soft materials. 4  Dynamics of liquids and soft matter Timedependent correlation functions. Inelastic diffusion of neutrons and measurement of the dynamic structure factor. Van Hove correlation functions. Principle of the detailed budget. Linear response theory. Answer function. Fluctuationdissipation theorem. Diffusion of particles. Diffusion coefficient. Speed correlation function. Hydrodynamics and collective modes. Scattering Brillouin. Memory functions. 5  Metastable states, subcooled liquids and glass transition for liquids and soft materials. Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and trends of correlation functions near the critical point. Subcooled liquids and glass transition. Angell diagram. Configurational entropy and Kauzmann temperature. The slow dynamics of subcooled liquids and soft matter and the theory of Mode Coupling. J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.
N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific. P. G. Debenedetti, Metastable Liquids, Princeton University Press. 
6  FIS/03  60        Core compulsory activities  ITA  

Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language 

20402228 
TRAINING
(objectives)
The internship / stage activity is a work that the student carries out under the guidance of a lecturer both in the university field, and in external sites affiliated with the University; provides the student with the ability to synthesize the acquired global knowledge, applying it to the drafting and elaboration of the thesis work

6          Other activities  ITA  
20410392 
Lingua inglese
(objectives)
Level B2 provides the student with a more indepth ability to communicate the conclusions, as well as the knowledge underlying them, of what has been learned, clearly and critically, also through the use in written and oral form of the English language and disciplinary lexicons, if necessary using the IT tools necessary for the presentation, acquisition and exchange of scientific data also through written documents, diagrams and diagrams. Ability to support a scientific discussion using the topics learned.

4  40        Other activities  ITA  
20401594 
FINAL EXAM
(objectives)
Demonstration by the student of the ability to deal with specific scientific problems, research and / or application of the concepts learned in the various disciplines of Physics

30          Final examination and foreign language test  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language 

20410581 
EXPERIMENTAL PHYSICS OF FUNDAMENTAL INTERACTIONS
(objectives)
The course provides the notions of experimental physics of elementary particles.
The course deals with both experimental and theoretical topics whose aim is to allow students to understand the experimental and theoretical path that led to the formulation of the Standard Model of fundamental interactions as we know it today. The fundamental experiments and discoveries starting from the discovery of elementary particles in cosmic rays up to the production of the vector bosons W and Z and of the Higgs boson are illustrated in detail. At the end of the course the student will have a broad view of particle physics from an experimental point of view, and sufficient knowledge of the theoretical tools necessary to understand its mechanisms. The course is supported by an exercise section whose aim is to reinforce the level of understanding of the topics covered and the calculation methods of the elementary processes, as well as allow students to apply the techniques learned for the calculation of some processes and the relationships between they exist. The course is aimed at all students and those who undertake a path of elementary particle physics that not, providing the basics of physics of elementary particles

Derived from
20410581 FISICA SPERIMENTALE DELLE INTERAZIONI FONDAMENTALI in Fisica LM17 DI MICCO BIAGIO, ORESTANO DOMIZIA
(syllabus)
Program:
(reference books)
1. Principles of invariance and conservation laws. 2. discrete and continuous symmetries; 3. relativistic equations: KleinGordon, Dirac 4. negative energy solutions, helicity, spin, solutions for zero mass, neutrinos 5. relativistic perturbation theory, interaction Hamiltonian, Feynman graphs, propagator as a Green function; 6. Lorentz transformations, laboratory and center of mass system, invariant mass, reaction kinematics, reaction threshold; 7. fields of interaction, Yukawa model; 8. primary and secondary cosmic rays, the muon: decay, mass and average life; 9. kinematics of decays, combination of angular moments, ClebschGordan coefficients, symmetry of the isospin; 10. decay widths and comparison between matrix elements, laws of storage; 11. phase spaction density, Scattering cross section, flux, factor of the space and of the invariant phases, scattering matrix elements; 12. the pion: charge, spin, parity, charge conjugation, isospin; 13. strange particles, hyperons, interaction of the K mesons; 14: strange baryons, mesonic and baryonic octets, SU (3) symmetry, hypercharge, Young's diagrams; 15: discovery of the antiproton, the antibaryons, the Delta resonance; 16: hadronic and mesonic resonances, model at Quarks; 17: representation of the mesons in the quarks model 18: potential scattering, solution of the Schroedingher equation for waves spherical; 19: diffusion and absorption cross section, unitarity limit, optical theorem; 20: resonant cross section, BreitWigner formula, baryon masses with GellMan Okubo formula; 21: the color quantum number, SU (3) representations of color, relationships between spin and SU (3) multiplets; 22: weak interaction, parity violation, madame Wu experiment; 23: oscillation of the K mesons, the Cabibbo angle, the GIM mechanism; 23: discovery of the charm and beauty quarks; 24: decay of D and B mesons, Feynman diagrams, isospin relations; 25: neutrino beams, neutrino flavor, discovery of the neutrino tau; 25: the accelerating machines e + e, hadronic impact section, the ratio R and the number of quarks and colors; 26: measurement of the helicity of the neutrino, discovery of the antineutrino; 27: deep inelastic scattering, parton distribution functions; 27: hadronic colliders, protonantiproton and protonproton: discovery of the W and Z bosons; 28: the Higgs boson 1. course notes, available on the course website;
2. F. Halzen, A. D. Martin, "An Introductory Course in Modern Particle Physics" 3. D. Scroeder, M. Peskin, "An Introduction to Quantum Field Theory" 4. S. Weinberg, "The Quantum Theory of Fields" 
8  FIS/01  64  16      Core compulsory activities  ITA 
20401904 
THEORETICAL PHYSICS I
(objectives)
To study classical electrodynamics in detail, to provide the elements of relativistic quantum mechanics. Provide the basics of field theory and QED

Derived from
20401904 FISICA TEORICA I in Fisica LM17 N0 DEGRASSI GIUSEPPE, Sanfilippo Francesco
(syllabus)
Special Relativity and Electromagnetism.
(reference books)
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and controvariant vectors, tensors, transformation law of the fields. Relativistic Dynamics: fourvelocity, fourmomentum, Minkowski force. Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields, electromagnetic field tensor, covariant formulation of the Maxwell equations, fourpotential, gauge invariance. Conservation laws: Maxwell stress tensor, energymomentum tensor, conservation of energy, momentum and angular momentum. Solution of the Maxwell equations for the fourpotential in the vacuum in the Lorentz gauge. Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect. Cerenkov effect. Relativistic Quantum Mechanics KleinGordon equation. Dirac equation, nonrelativistic limit. Covariance of the Dirac equation. Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality. Quantum Field Theory Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators. Heisenberg representation. Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization. Electromagnetic field, covariant quantization. Global and local invariance. Interaction picture. Smatrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields. Quantzation of the electromagnetic field. Feynman diagrams and rules in QED. Treelevel processes: e+e  mu+ mu, scattering by an external field. V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons. 
8  FIS/02  46  22      Core compulsory activities  ITA 
20402210 
CONDENSED MATTER PHYSICS
(objectives)
The course aims to apply the methods of mechanics quantum to the description of the fundamental properties of solid matter

Derived from
20402210 FISICA DELLA MATERIA CONDENSATA in Fisica LM17 N0 GALLO PAOLA, LUPI LAURA
(syllabus)
Overview on condensed matter. Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: xrays, electrons and neutrons. Quasicrystals. Classification of crystalline solids and bonds. Adiabatic approximation (BornOpenheimer). Lattice vibrational dynamics, phonons. Specific heats of Einstein, Debye and electronic. Electrons in periodic potentials: the Bloch theorem. Theory of the free electron in metals. The many electrons Hamiltonian and one electron approximations: Hartree and Hartree Fock equation. Band theory in crystals: Tight Binding method and the nearly free electron approximation. Electronic properties of relevant crystals. Transport in metals. Intrinsic and doped semiconductors and transport. pn junction. Superconductivity.
(reference books)
Giuseppe Grosso and Giuseppe Pastori Parravicini Solid State Physics Academic Press
others: Neil W. Ashcroft N. David Mermin Solid State Physics Saunders College Charles Kittel Introduzione alla Fisica Dello Stato Solido Casa Editrice Ambrosiana WRITTEN NOTES, PRESENTATIONS AND EXERCISES will be published on the course web site http://webusers.fis.uniroma3.it/~gallop/ 
8  FIS/03  60  20      Core compulsory activities  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  

20402211 
COMPLEMENTS OF MATHEMATICAL METHODS FOR PHYSICS
(objectives)
The aim of the course is to learn the basic tools to deal with Lie algebras and their representations and to acquire computer calculation techniques,both for symbolic and for numerical calculations. Topics of the course
will be dealt with using either Wolfram Language and Python or alternative computer languages preferred by the student.

Derived from
20402211 COMPLEMENTI DI METODI MATEMATICI DELLA FISICA in Fisica LM17 N0 FRANCESCHINI ROBERTO
(syllabus)
Group Theory (CA)
(reference books)
SU(2) and SU(3) The Killing Form Simple Lie Algebras Representations Simple Roots and the Cartan Matrix The Classical Lie Algebras The Exceptional Lie Algebras Casimir Operators and Freudenthal’s Formula The Weyl Group Weyl’s Dimension Formula Reducing Product Representations Subalgebras Branching Rules Numerical Methods Refresh on Probability and Random variables Refresh on Measurement, uncertainty and its propagation Refresh on Curvefitting, leastsquares, optimization Classical numerical integration, speed of convergence Integration MC (Mean, variance) Sampling Strategies Applications Propagation of uncertainties Generation according to a distribution Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html Robert Cahn  SemiSimple Lie Algebras and Their Representations  Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S.  Introduction to Monte Carlo methods arXiv:hepph/0006269 Taylor, J.  An introduction to error analysis  University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre Dubi, A.  Monte Carlo applications in systems engineering  Wiley Disponibile nella biblioteca Scientifica di Roma Tre readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html 
6  FIS/02  34  18      Core compulsory activities  ITA  
20410054 
Environmental Physics
(objectives)
The course aims at providing students with fundamental notions for understanding the interactions between the atmosphere, the ocean, and the earth's surface, nad the main physicalchemical connected processes, with particular respect to electromagnetic radiation  matter interactions. The course intends to deal with the interconnection and inter / multidisciplinary aspects of the involved phenomena, and to provide information on the measurement principles of various properties of the atmosphere, the ocean, and the Earth's surface, and in particular on remote sensing observations.

DI SARRA ALCIDE
(syllabus)
The course is designed to provide students with the fundamental information for understanding the interactions between the atmosphere, the ocean, and the earth's surface, the main physicalchemical processes connected, and the impacts on air and sea quality. The course intends to deal with the interconnection and inter / multidisciplinary aspects of the phenomena involved and to provide information on the measurement principles of various properties of the atmosphere and the ocean.
(reference books)
Course program Structure and composition of the atmosphere. Atmospheric dynamic processes. Main gases and trace gases. Particulate matter and clouds. Emissions and chemical reactions in the atmosphere. Chemical reactions relevant to air quality. Planetary limit layer and its evolution. Structure and composition of the ocean. Salinity, temperature, density. Oceanic dynamic processes. Scrambled layer, thermocline. Chemical composition and marine pollutants. Exchanges of energy and matter between atmosphere, ocean, earth. Elements on the hydrological cycle and the carbon cycle. Techniques and methods of measurement of some atmospheric and oceanographic parameters. Hartmann, D.L., Global Physical Climatology. Elsevier, 2016.
Stewart, R. H., Introduction to physical oceanography, 2008. http : / /hdl .handle .net /1969 .1 /160216. Wallace, J.M., e P. V. Hobbs, Atmospheric Science: An Introductory Survey. Academic Press, 2006. 
6  FIS/07  48        Related or supplementary learning activities  ITA  
20402213 
ELEMENTS OF EARTH PHYSICS AND OF ENVIRONMENT
(objectives)
The course is structured on the basic concepts of Solid and Fluid Earth Physics in order to provide the student with a coherent and updated picture of this discipline, both from a theoretical and an experimental point of view

PLASTINO WOLFANGO
(syllabus)
Gravity
(reference books)
The Earth’s size and shape. Gravitation. The Earth’s rotation. The Earth’s figure and gravity. Gravity anomalies. Interpretation of gravity anomalies. Isostasy. Rheology. Seismology Elasticity theory. Seismic waves. Earthquake seismology. Seismic wave propagation. Internal structure of the Earth. Earth’s age and thermal properties Geochronology. The Earth’s heat. Geomagnetism and paleomagnetism The Physics of magnetism. Rock magnetism. Geomagnetism. Paleomagnetism. Fundamentals of Geophysical Fluid Dynamics Time derivatives for fluids. The mass continuity equation. The momentum equation. The equation of state. Thermodynamic relations. Thermodynamic equation for fluids. Compressible and incompressible flow. The energy budget. Physics of the Atmosphere Heterogeneous systems. Transformations of moist air. Hydrostatic equilibrium. Static stability. Radiative transfer. Largescale motion. Wave propagation. The general circulation. Dynamic stability. Physics of the Ocean Oceans and Seas. Atmospheric influences. The oceanic heat budget. Wind driven ocean circulation. Deep circulation in the ocean. Equatorial processes. Ocean waves. Coastal processes and tides. Stacey F.D. and Davis P.M.  Physics of the Earth. Cambridge University Press, 2008  ISBN:9780521873628
Vallis G.K.  Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, 2006  ISBN:9780521849692 

ITA  
20410042 
TERRESTRIAL PHYSICS
(objectives)
The main objectives of the course are three: 1. To develop in the student the conviction of the need for a deep knowledge of Physics for the different applications necessary for understanding the Earth System.2. Give the student a specific knowledge of the physical mechanisms of the interior of the planet. 3. To make the student aware of an interdisciplinary and multidisciplinary approach and the different methods useful for the study of the Earth System

PETTINELLI ELENA
(syllabus)
Earth in the Solar System
(reference books)
TitusBode Law. Terrestrial and gaseous planets. Notes on the formation of the solar system. Elements of chemistry of the solar system. Geochemical classification of the elements. Formation and differentiation of planets The Earth as a Planet Definition of planet. Kepler's laws. General features: liquid water, atmosphere, crustal dichotomy, magnetic field, internal dynamics. Earth's mass, density and moment of inertia The problem of estimating the average density of the Earth: historical notes (from Newton to Poynting). Cavendish's experiment in a modern way. Estimate of the mass of the Earth and planets  Average density of the Earth. Recalling the moment of inertia. Tensor of moments of inertia. Ellipsoid and spheroid. Moment of inertia of a solid sphere with constant density. Moments of inertia and models of planetary structures. Earth's shape and gravity The shape (figures) of the Earth .. Oblate ellipsoid and polar crushing. Earth shape and topography. Earth shape and variations of g. Acceleration and gravitational potential. Gravitational potential: Laplace equation. Gravitational potential in spherical coordinates. Gravitational potential of a solid sphere with constant density. General solution of the Laplace equation in spherical coordinates. Legendre polynomials. Spherical harmonics and Stokes coefficients. MacCullagh equation and moments of inertia. Ellipticity of the shape (figures) of the Earth. The acceleration ratio m (acceleration ratio). The geopotential. Relationship between J2, J4, m and f. Calculation of the inertia ratio for the Earth. Gravity on the reference spheroid. Geocentric and geographical latitude. Clairaut formula. Normal gravity. The geoid. Measurements of g. Absolute and relative measures. Corrections to the extent of g. Anomalies in open air and Bouguer. Nonuniqueness of the anomalies of g. Isostasy. Isostatic anomalies. Vertical movements of the crust. Isostatic compensation. Isostatic adjustments and coat viscosity. Satellite geoid measurements. Geoid ripples. Tides and land rotation Origin of the tides. Tidal potential. Components of the lunar tidal acceleration. Combination of lunar and solar tides. Terrestrial tides. Tidal friction and deceleration of terrestrial and lunar rotation. Euler nutation and Chandler swing. Solarsolar precession. Notes on the properties of minerals and rocks Crystalline structure of minerals. The rocks. Classification of rocks. Sedimentary, igneous and metamorphic rocks. Eutectics and solid solutions. Terrestrial magnetism: History  from Petrus Peregrinus to Gauss. The magnetism of the rocks Physics of magnetism. Ampere equivalence principle. Review of atomic magnetic moments. Magnetic susceptibility. Magnetic properties of matter. Diamagnetism (classical theory). Paramagnetism (classical theory). Ferromagnetism. Ferrimagnetismo. Antiferromagnetism. Parasitic ferromagnetism. Magnetic minerals. Magnetism of the rocks. Titanomagnetites and magnetic series. Magnetization of rocks. Types of magnetization. Thermoremaining magnetization (TRM). Remaining chemical magnetization (CRM). Remaining Debris Magnetization (DRM). Notes on Paleomagnetism. Earth's magnetic field The observables of the CMT. General characteristics of the CMT. Laplace equation and CMT potential. Gauss coefficients. CMT modeled with dipoles. The terrestrial dipolar field. CMT best fit  inclined eccentric dipole. Power spectrum of the CMT. Estimated depth of the source of the main field. Secular variation. External sources of the CMT. Earth core composition. CMT models. Bullard dynamo. Selfexcited dynamo model. The magnetohydrodynamic approach. Magnetohydrodynamics equations. Hydrodynamic magneto models. Magnetic measurements. Precession magnetometer. Magnetic anomalies and corrections. Terrestrial heat Earth's energy budget. Heat transmission within the Earth: conduction, convection, radiation and advection. Internal heat sources. Original heat; radiogenic heat; other heat sources. Conduction equation (Fourier equation). Heat conduction equation in three dimensions. Thermal diffusion. Adjective term. Balance geotherm. Notes on the transport of heat in the oceanic and continental lithosphere. Time scale of the conductive heat flow. Adiabatic thermal gradient. Melting point gradient. Geothermal diagrams inside the Earth. Internal structure of the Earth AdamsWilliamson equation. Density trend with depth. Unzipped density. The mineralogical phases of the coat. Compositional model of the Earth. Structure and asymmetries of the Earth's core. Profiles of v, rho, g and P within the Earth. Bullen model and Preliminary Reference Earth Model (PREM). Stacey, F. D., and Davis, P. M. (2008) Physics of the Earth, Cambridge University Press.
Fowler, C. M. R. (2005). The Solid Earth, Cambridge University Press. 
6  FIS/06  48        Core compulsory activities  ITA  
20410047 
Mechanics of Continuous Media in Physics of the Earth and Environment
(objectives)
Provide the student with the fundamental physical and mathematical tools for describing continuous mechanical systems with particular attention to applications in terrestrial and environmental physics

MATTEI ELISABETTA
(syllabus)
Surface forces and volume forces. Traction vector or strain vector.
(reference books)
Traction applied to a free body. Cauchy's relation and Cauchy's tetrahedron. Stress tensor property. Diagonalization of stress matrix Principal axes and planes. Principal stresses. Invariantes. Maximun shear stesses. Spherical, deviatory, hydrostatic, lithostatic stress. The tensor deformation. The antisymmetric tensor of rigid rotations. Principal deformations. Dilatation. Relationships between stress and deformation. Constitutive equations. Rheological function. Linear elasticity. Hooke's Law Generalized. Hooke's law for homogeneous and isotropic media. DuhamelNeumann equations. Stressdependent rheological function, deformation and time. Linear viscoelasticity. Timedeformation. Boltzmann Linear Solids with Memory Mechanism. Constitutive equations. Boltzmann's IntegralDifferential Equation. Creep and relaxation functions, complex module and quality factor. Linear viscoelastic models of Maxwell, KelvinVoigt, SLS. Dynamic theory of elasticity. Elastic waves. HelmholtzLamé's elastic potential and theorem. Plane and Spherical waves. Horizontal and vertical slowness. Volume waves. Waves P, S, SH, SV. Phase velocity and Group velocity. Partition and conversion of seismic energy to a surface of discontinuity. Reflection and transmission coefficients. Geometric spreading. Attenuation and scattering of a seismic wave. Surface Waves. Rayleigh and Love Waves. Dispersion of surface waves. Equation and dispersion curve. Fundamental and overtones mode. Free oscillations of the Earth. Spheroidal and toroidal (or torsional) modes. Seismology and earth structure. Refraction seismology. Reflection seismology. Travel times. Travel times In a layered Earth. Direct waves, head wave, Reflected wave, diffracted wave. Shadow zones. Dromocron. Seismic waves in a spherical earth. Short and longterm seismometers. Seismograms and their interpretation. Determination of the epicenter. Volume waves nomenclature. Determination of Hypocentric parameters. The inverse problem. Origin Time. The Seismic Source: radation pattern and Focal Mechanism. Seismic: focal point and focal mechanism. Seismic Moment and Magnitude. Determination of the seismic moment. Earthquake magnitude. Local magnitude, for volume waves, for the Superficial waves. Saturation of magnitude scales. Seismic energy and magnitude momentum.  An introduction to seismology: earthquakes and earth structure. Stein and Wysession. Blakwell publishing.
 Terremoti e onde. Metodi e pratica della sismologia moderna. Zollo e Emolo. Liguori.  Modern global seismology. Lay Thorne AND Terry C. Wallace. Vol. 58. Elsevier, 1995. 
6  FIS/06  48        Related or supplementary learning activities  ITA 
Course  Credits  Scientific Disciplinary Sector Code  Contact Hours  Exercise Hours  Laboratory Hours  Personal Study Hours  Type of Activity  Language  

20410048 
METODI SPERIMENTALI DI GEOFISICA
(objectives)
Investigations of the interior and exterior of the earth and planets. Methods of prospecting and probing the earth and circumterrestrial space. Laboratory measurements in situ and on board satellites

PETTINELLI ELENA
(syllabus)
Experimental methods of geophysics
(reference books)
Course program – A, Academic Year 2018/2019 Recalls on the treatment of experimental data and estimate of uncertainties. Expression of the uncertainties of measure in accordance with the GUM (Guide of the expression of uncertainty in measurements  NIST, 2008). Recalls on data analysis of geophysical interests in MATLab. Laboratory measurement techniques, in the field and from satellite. Electrical and magnetic properties of geomaterials. Electrics and magnetic measuraments in time and frequency domains. Activities of the laboratory: use of the LCR bridge and the Vector Network Analyzer for the measurement of dielectric permittivity and magnetic permeability. Electromagnetic propagation in geomaterials. Subsurface radar: theoretical bases and applications in environmental field. Activities of the laboratory: techniques of data analysis and estimate of physical parameters; methods of inversion. Mechanical properties of geomaterials. Propagation measurements of P waves in rock samples. Activity of laboratory: Analysis of signals in frequency and time domains. Estimation of the speed of mechanical waves and elastic parameters. Lecture notes;
Ground Penetrating Radar – H.M. Jol, 2009, Elsevier; Introduction to the Physics of Rocks Y. Guéguen and V. Palciauskas, 1994, Princeton University Press. 
8  FIS/06  28    54    Core compulsory activities  ITA  
