Program:

1. Principles of invariance and conservation laws.
2. discrete and continuous symmetries;
3. relativistic equations: Klein-Gordon, 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, Clebsch-Gordan 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 anti-proton, the anti-baryons, 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, Breit-Wigner formula, baryon masses with Gell-Man 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 anti-neutrino;
27: deep inelastic scattering, parton distribution functions;
27: hadronic colliders, proton-anti-proton and proton-proton: 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"

Program:

1. Principles of invariance and conservation laws.
2. discrete and continuous symmetries;
3. relativistic equations: Klein-Gordon, 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, Clebsch-Gordan 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 anti-proton, the anti-baryons, 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, Breit-Wigner formula, baryon masses with Gell-Man 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 anti-neutrino;
27: deep inelastic scattering, parton distribution functions;
27: hadronic colliders, proton-anti-proton and proton-proton: 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"

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential 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
Klein-Gordon equation. Dirac equation, non-relativistic 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. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level 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.

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential 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
Klein-Gordon equation. Dirac equation, non-relativistic 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. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level 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.

Overview on condensed matter. Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: x-rays, electrons and neutrons. Quasicrystals. Classification of crystalline solids and bonds. Adiabatic approximation (Born-Openheimer). 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. p-n junction. Superconductivity.

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/

Exercises on the following topics:
Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: x-rays. 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.

Group Theory (CA)

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 Curve-fitting, least-squares, 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 - Semi-Simple 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:hep-ph/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

- SPECIAL RELATIVITY. VECTORS AND TENSORS. METRIC TENSOR. ENERGY-MOMENTUM TENSOR.
- 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 ROBERTSON-WALKER METRIC.
- FRIEDMAN EQUATIONS. NEWTONIAN LIMIT.
- COSMOLOGICAL REDSHIFT. COSMOLOGICAL HORIZONS. CO-MOVING 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. RE-IONIZATION.
- 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]

Radiative processes in Astrophysics: Transfer Equation, Bremsstrahlung, Synchrotron Emission, Inverse Compton Effect, Pairs Production, Cherenkov Effect
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

1.
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

Stellar Observations
Magnitude of a star. Brightness intensity. Apparent and relative magnitude. Black body spectrum. Wien and Stefan-Boltzmann laws. The colors of stars. Optical Depth. Radiation transport equation. Eddington-Barbier approximation. Gray atmosphere. Definition of photosphere and effective temperature. Hertzprung-Russell and Color-Magnitude 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: bound-bound, , bound-free, and free-free. Kramer's opacity. Thomson scattering. Electronic conduction. Relative importance of the various types of opacity in the density-temperature 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. Convection-related uncertainties. Free parameter calibration. Problems related to turbulence and non-local 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 non-relativistic case. Crystallization. Neutronization. Relative importance of the various types of pressure in the density-temperature 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 proton-proton 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 pre-main sequence stars. Hayashi lines and their physical meaning. Stratification of entropy into radiative and convective stars. Pre-main sequence evolutionary tracks in the HR diagram. The Kelvin-Helmotz 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. "Disk-locking" and magnetic braking.

Core hydrogen burning
Main sequences (MS) of open and globular clusters. Mass-Luminosity 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
Post-MS evolution. Giant expansion. The Schonberg-Chandrasekhar instability. Degeneracy of the helium core in low mass models. First dredge-up: 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 low-mass stars up to the red giant tip. The role of the CNO shell. Core mass - luminosity relationship for low-mass stars. The role of neutrinos for the determination of the temperature peak. Helium Flash. Flash thermodynamics. The role of electron degeneracy. Mini-flash episodes. Comparison of pre- and post-flash 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 dredge-up. 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 Dredge-up. Llithium-rich stars. Carbon stars. Changes in the surface chemistry of AGB stars of different mass. Super-AGB 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: mass-radius 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 Period-Luminosity relationships.


Stellar clusters
The spatial distribution of stellar clusters across the Milky Way. Distribution of stars in clusters in the color-magnitude plane. Differences between open and globular clusters. The isochrone fitting method: turn-off 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. Oxygen-sodium and magnesium-aluminum anti-correlations. 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 Wolf-Rayet stars. Supernovae: Supernovae observations of types Ia, Ib, Ic and II. Post-carbon evolutionary phases: formation of a degenerate core. Collapse of the core. Core photo-disintegration .Explosive Mechanisms.

Title: Stellar structure and evolution
Authors: Kippenhahn, Weigert
Springer-Verlag 1990

Title: Introduction to stellar Astrophysics (vol. 2)
Author: E. Bohm-Vitense
Cambridge University Press 1992

Title: Introduction to stellar Astrophysics (vol. 3)
Author: E. Bohm-Vitense
Cambridge University Press 1992

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:
- 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 Sachs-Wolfe effect. Secondary effects. -
- Cosmic backgrounds in different energy bands: Radio, X-ray and gamma-ray
- Secondary anisotropies. The Gunn-Peterson effect, cosmic reionization, Ly-alpha forest and Sunayev-Zel'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. Press-Schechter theory and its extension.
- Peculiar velocities, distance indicators and their calibrations.
- Gravitational lensing: Theory and observations. Micro-lensing. 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.

COMPACT OBJECTS: WHITE DWARFS, NEUTRON STARS, THE CHANDRASEKHAR LIMIT, PULSARS, BLACK HOLES
ACCRETION: THEORY, EDDINGTON LIMIT, ACCRETION DISKS
X-RAY BINARIES: CLASSIFICATION AND PHENOMENOLOGY, CATACLYSMIC VARIABLES, LOW-MASS AND HIGH-MASS X-RAY BINARIES, BLACK HOLE CANDIDATES
ACTIVE GALACTIC NUCLEI: CLASSIFICATION AND PHENOMENOLOGY, X-RAY AND GAMMA-RAY 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]

Program:

1. Principles of invariance and conservation laws.
2. discrete and continuous symmetries;
3. relativistic equations: Klein-Gordon, 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, Clebsch-Gordan 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 anti-proton, the anti-baryons, 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, Breit-Wigner formula, baryon masses with Gell-Man 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 anti-neutrino;
27: deep inelastic scattering, parton distribution functions;
27: hadronic colliders, proton-anti-proton and proton-proton: 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"

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential 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
Klein-Gordon equation. Dirac equation, non-relativistic 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. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level 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.

Overview on condensed matter. Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: x-rays, electrons and neutrons. Quasicrystals. Classification of crystalline solids and bonds. Adiabatic approximation (Born-Openheimer). 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. p-n junction. Superconductivity.

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/

Group Theory (CA)

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 Curve-fitting, least-squares, 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 - Semi-Simple 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:hep-ph/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

Electronic properties of selected crystals
Reminds on band structure calculation methods. Electronic structure of molecular and ionic solids. Band structure of II-VI, III-V 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 electron-hole pairs in semiconductors. Continuity equation. Recombination times and diffusion length. Current voltage characteristics of the p-n junction. Metal-semiconductor 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 phonon-assisted transitions. Two-photon 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 Haas-van Alphen effect. Magneto-resistivity 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 closed-shell 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. Curie-Weiss 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.

Ashcroft-Mermin: "Solid State Physics"
Grosso-Pastori-Parravicini: "Solid State Physics"
Sze- Physics of Semiconductor Devices

- Fluctuation-dissipation theorem and linear response theory.
-Green functions at zero temperature. Lehmann decomposition. Analytical properties.
- Perturbative development and Feynman diagrams. Dyson equation.
- Green functions at finite temperature: Matsubara technique.
- Hartree-Fock theory and RPA approximation. Thomas-Fermi 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 Landau-Ginzburg 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 Many-Body Physics, Cambridge University Press 2015.

Eye and perception. History of microscopy.
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. Sample-probe 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 open-access 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

see the professor's profile

see the professor's profile

Basic concepts and potential scattering in atomic collision.
Electron-atom 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 three-step 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, Radiation-matter 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)

Program:

1. Principles of invariance and conservation laws.
2. discrete and continuous symmetries;
3. relativistic equations: Klein-Gordon, 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, Clebsch-Gordan 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 anti-proton, the anti-baryons, 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, Breit-Wigner formula, baryon masses with Gell-Man 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 anti-neutrino;
27: deep inelastic scattering, parton distribution functions;
27: hadronic colliders, proton-anti-proton and proton-proton: 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"

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential 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
Klein-Gordon equation. Dirac equation, non-relativistic 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. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level 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.

Overview on condensed matter. Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: x-rays, electrons and neutrons. Quasicrystals. Classification of crystalline solids and bonds. Adiabatic approximation (Born-Openheimer). 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. p-n junction. Superconductivity.

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/

Group Theory (CA)

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 Curve-fitting, least-squares, 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 - Semi-Simple 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:hep-ph/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

SECTION B
- 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
- b-jet identification and top quark measurements
- Complex detectors: magnetic spectrometers, particle identification, large detectors
- Scintillators and optical devices (PMT, APD, SiPM). Solid state detectors. Multi-wire 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 [Springer-Verlag 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

SECTION B
- 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
- b-jet identification and top quark measurements
- Complex detectors: magnetic spectrometers, particle identification, large detectors
- Scintillators and optical devices (PMT, APD, SiPM). Solid state detectors. Multi-wire 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 [Springer-Verlag 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

SECTION A
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. Theta-tau puzzle.
- Quark model, mentions
- Parton model, quark and anti-quark density

c) Electro-weak 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 electro-weak 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 B-factories 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 [Springer-Verlag 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

SECTION A
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. Theta-tau puzzle.
- Quark model, mentions
- Parton model, quark and anti-quark density

c) Electro-weak 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 electro-weak 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 B-factories 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 [Springer-Verlag 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

Feynman diagrams. Tree-level processes. Discrete symmetry
Feynman diagrams and cross-sections. Bhabha and Compton scattering. Gauge invariance.
Chiral and Majorana representations for the matrices. Parity, charge conjugation and time-reversal.

Radiative Corrections
Divergent behavior of an integral. Primitively divergent diagrams. Pauli-Villars regularization.
Coupling, mass and wave-function 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
Yang-Mills 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

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
(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 - Springer-Verlag
W. Blum, L. Roland - Particle Detection with Drift Chambers - Springer-Verlag
T. Ferbel - Experimental Techniques in High-Energy Nuclear and Particle Physics
F. Sauli - Principles of operation of multiwire proportional and drift chambers
I. Lombardo - Problemi di fisica nucleare e subnucleare - Zanichelli

PROGRAM OF LESSONS IN THE CLASSROOM

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 - Springer-Verlag
W. Blum, L. Roland - Particle Detection with Drift Chambers - Springer-Verlag
T. Ferbel - Experimental Techniques in High-Energy Nuclear and Particle Physics
F. Sauli - Principles of operation of multiwire proportional and drift chambers

see the professor's profile

see the professor's profile

Program:

1. Principles of invariance and conservation laws.
2. discrete and continuous symmetries;
3. relativistic equations: Klein-Gordon, 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, Clebsch-Gordan 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 anti-proton, the anti-baryons, 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, Breit-Wigner formula, baryon masses with Gell-Man 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 anti-neutrino;
27: deep inelastic scattering, parton distribution functions;
27: hadronic colliders, proton-anti-proton and proton-proton: 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"

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential 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
Klein-Gordon equation. Dirac equation, non-relativistic 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. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level 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.

Overview on condensed matter. Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: x-rays, electrons and neutrons. Quasicrystals. Classification of crystalline solids and bonds. Adiabatic approximation (Born-Openheimer). 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. p-n junction. Superconductivity.

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/

Group Theory (CA)

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 Curve-fitting, least-squares, 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 - Semi-Simple 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:hep-ph/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

Feynman diagrams. Tree-level processes. Discrete symmetry
Feynman diagrams and cross-sections. Bhabha and Compton scattering. Gauge invariance.
Chiral and Majorana representations for the matrices. Parity, charge conjugation and time-reversal.

Radiative Corrections
Divergent behavior of an integral. Primitively divergent diagrams. Pauli-Villars regularization.
Coupling, mass and wave-function 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
Yang-Mills 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

see profile of the teacher holding the course

see profile of the teacher holding the course

- SPECIAL RELATIVITY. VECTORS AND TENSORS. METRIC TENSOR. ENERGY-MOMENTUM TENSOR.
- 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 ROBERTSON-WALKER METRIC.
- FRIEDMAN EQUATIONS. NEWTONIAN LIMIT.
- COSMOLOGICAL REDSHIFT. COSMOLOGICAL HORIZONS. CO-MOVING 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. RE-IONIZATION.
- 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]

Introductive Lectures:
Green Functions, Feynman Diagrams, Exponentiation of disconnected diagrams, IN and OUT states, S-Matrix, S-Matrix in terms of Feynman diagrams, Kaellen-Lehmann Spectral Representation, LSZ Reduction Formula, Optical Theorem.

Renormalization:
Superficial Divergence Degree of Diagrams, Renormalized Perturbation Theory, Callan-Symanzik 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 (Faddeev-Popov Method), Dirac Field Quantization, Quantization of Non-abelian Gauge Theories, Ghosts.

Michael E. Peskin, Daniel V. Schroeder "An Introduction to Quantum Field Theory";
Franz Mandl, Graham Shaw "Quantum Field Theory".

Introductory notions
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 (one-form). Cotangent space and corresponding basis. Coordinate transformation of the components of a one-form. 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, one-forms 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 p-forms 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 right-invariant vectors. Structure constants. Examples of Lie groups. Maurer-Cartan forms. Maurer-Cartan’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, torsion-free 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, G-atlas, G-structure. 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 2-form 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.
Levi-Civita 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, self-parallel 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 Robertson-Walker 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. Scalar-tensor 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 Cosmology-principles and
application of the general theory of relativity (John
Weiley & Sons, 1972);
6. people.sissa.it/~percacci/lectures/general/index.html

Program:

1. Principles of invariance and conservation laws.
2. discrete and continuous symmetries;
3. relativistic equations: Klein-Gordon, 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, Clebsch-Gordan 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 anti-proton, the anti-baryons, 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, Breit-Wigner formula, baryon masses with Gell-Man 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 anti-neutrino;
27: deep inelastic scattering, parton distribution functions;
27: hadronic colliders, proton-anti-proton and proton-proton: 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"

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential 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
Klein-Gordon equation. Dirac equation, non-relativistic 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. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level 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.

Overview on condensed matter. Geometric description of crystals: direct and reciprocal lattices and Brillouin zone. Scattering of particles by crystals: x-rays, electrons and neutrons. Quasicrystals. Classification of crystalline solids and bonds. Adiabatic approximation (Born-Openheimer). 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. p-n junction. Superconductivity.

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/

Group Theory (CA)

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 Curve-fitting, least-squares, 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 - Semi-Simple 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:hep-ph/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

- Fluctuation-dissipation theorem and linear response theory.
-Green functions at zero temperature. Lehmann decomposition. Analytical properties.
- Perturbative development and Feynman diagrams. Dyson equation.
- Green functions at finite temperature: Matsubara technique.
- Hartree-Fock theory and RPA approximation. Thomas-Fermi 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 Landau-Ginzburg 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 Many-Body Physics, Cambridge University Press 2015.