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.

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

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

L.S. Sparke and J.S. Gallagher
Galaxies in the Universe - An Introduction. Cambridge University Press

see the profile of the lecturer

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

§I. Introduction: inertia and covariance

Galilean Relativity and Special Relativity. The Equivalence Principle. Motivations for general covariance. Local inertial frames.

§II. Dynamical spacetime: basics of General Relativity

Curvilinear coordinates. Vectors and tensors under general coordinate transformations. Parallel transport and Christoffel symbols. Covariant derivatives and metric compatibility. Covariantly conserved vectors and conserved vector densities. Transformation of the Christoffel symbols. Ricci's theorem. Geodesics and their Newtonian limit. Time-like, null and space-like curves. Normal coordinates and local inertial frames. Covariant derivation along curves. Riemann curvature tensor. Algebraic properties. Bianchi identities. Local inertial frames. Characterisation of flat spaces. Geodesic deviation. Einstein-Hilbert action and equations of motion. The Palatini identity. Non-dynamical sources: contracted Bianchi identity, matter energy-momentum tensor and covariant conservation. Minimal coupling to scalar fields and to Maxwell fields.

§III. Linear approximation and gravitational waves

Motivations. Weak fluctuations over flat space-time: linearised Riemann tensor and its abelian gauge invariance. Equations of motion: de Donder gauge and gravitational waves. Comparing to Maxwell's theory.

§IV. Isometries and maximally symmetric spaces

Symmetries of tensors: form-invariance. Killing equations. Integrability condition and maximal number of isometries. The Lie derivative. Killing vectors and conservation laws. The example of Minkowski space. Translational isometries.

§V. Basics of the Schwarschild solution

Schwarzschild metric. Spherical symmetry and Birkhoff's theorem (without proof). Killing vectors of Schwarzschild's metric. Gravitational redshift.

-Carroll S Spacetime and Geometry: An Introduction to General Relativity (Addison-Wesley 2014/Cambridge University Press, 2019)
-Dirac P A M General Theory of Relativity (Princeton University Press, 1996)
-Hartle S Gravity: An Introduction to Einstein's General Relativity (Cambridge University Press, 2021)
-Rovelli C, General Relativity - the Essentials, (Cambridge University Press, 2021).
-Weinberg S, Gravitation and Cosmology - principles and applications of the general theory of relativity, (John Wiley \& Sons, 1972).

- Cosmological Principle And Robertson-Walker Metric
- Friedmann Equations
- The Standard Cosmological Model
- Redshift, Cosmological Distances And Cosmological Horizons
- Cosmological Parameters And Their Measurement
- Classical Cosmologial Tests: Hubble Test. Angular Diameter Test. Counts
- Cosmological Constant
- Cosmic Fluids And Their Equation Of State
- Thermal History Of The Universe: Decoupling, Recombination
- Matter-Antimatter Asymmetry
- Beyond Standard Model: Horizon And Flatness Paradoxes, Introduction To Cosmic Inflation
- Dark Matter
- Brief History Of The Universe
- Cosmological Nucleosynthesis
- Matter Dominated Era. Reionization.
- Fcosmic Microwave Background
- Jeans Theory Of Gravitational Instability
- Evolution Of Cosmic Structures
- Spectrum Of Density Perturbations. Linear And Non-Linear Evolution Of The Cosmic Density Field
- Spherical Collapse And Press & Schechter Theory
- Introduction To Numerical Approaches To Structure Formation: N-Body Simultaions
- Key Processes In Galaxy Formation
- Introduction To Open Problems In Structure Formation

Coles P., Lucchin F. Cosmology [Wiley 2000]
Peebles P.J.E. 1993. Principles of Physical Cosmology [Princeton Series in Physics 1993]

50 hours in front

•Brief references to general relativity and Einstein's equation
•Robertson-Walker metric
•Hubble's law and Hubble tension
•Redshift
•Cosmological distances
•The cosmological constant
•Friedmann and Einsten-de Sitter models
•Cosmic Microwave Background
•Jeans theory for gravitational instability
•Application of Jeans theory in Cosmology: linear evolution
•Formation of Structures I: case only baryons
•Formation of Structures II: case with also non-baryonic matter
•Perturbation spectrum, filters and transfer functions
•Covariance functions
•Theory and observations related to linear theory: CMB fluctuations
•Large-scale structure of the Universe: statistical analysis of the distribution of galaxies
•Non-linear evolution of perturbations
•Virialized structures: the theory of Press and Schechter and its extension
•Light matter and dark matter: the problem of bias.
•The Euclid mission
•Notes on extragalactic radio sources


Completion of the 64 hours: study of the article
"Hosts and Environments: a (large-scale) radio history of AGN and star-forming galaxies"
(https://link.springer.com/article/10.1007/s00159-022-00142-1)

Coles P., Lucchin F. Cosmology [Wiley 2000] - Testo primario

Peacock J. Physical Cosmology. Cambridge Univ.Press

Padmanabhan t: structure fornation in the universe, cambridge university press

"Cosmology" di Weinberg (Oxford University Press)

A number of scientific papers provided by the teacher 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]

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".

§I.Relativistic Field Theory

The Poincaré Group. Symmetries: global vs local. Noether's first and second theorems and conservation laws. The canonical stress-energy and angular momentum tensors. Improvements. Belinfante's argument and symmetric energy-momentum tensor. Local symmetries and conserved quantities.

§II.Gravity as a relativistic field theory

Particles and fields in Special Relativity. Irreps of the Poincaré group: Wigner's induced representation method. Massless particles: ISO(D-2) little group and gauge invariance. From relativistic massless spin-2 particles to full GR. Fierz-Pauli quadratic Lagrangian. Nöther method and non-linear completions. Nöther's construction of Yang-Mills Lagrangian. The transverse-traceless gravitational cubic vertex. Weinberg's Equivalence Principle from relativistic invariance of the S matrix. Spin and the sign of static forces.

§III.Elements of differential geometry

Topological spaces. Manifolds. Diffeomorphisms. Tangent spaces and vectors. Coordinate basis. Derivative operators on manifolds. Levi-Civita connection. Torsion. Differential forms: definition, wedge product, interior and exterior derivatives, Hodge dual. Lie derivative of forms and Cartan's formula. Yang-Mills theory in the language of forms. Weyl tensor. Riemann and Weyl tensors in various dimensions: counting components for irreps of GL(D). Conformal transformations of the metric tensor. Conformally flat spaces. Conformally coupled scalar fields.

§IV. The Cartan-Weyl formulation of GR and Fermionic couplings

Local inertial frames. The frame field and its relation to the metric field. Local Lorentz transformations. The spin connection. The vielbein postulate. Torsion constraint and second-order formulation. The contorsion tensor. Local Lorentz curvature. Gravity as a gauge theory of the Poincaré algebra. Connection one-forms on the Poincar\'e algebra. Local Poincar\'e transformations. Torsion and curvature over the Poincar\'e algebra. First-order formulation and Cartan-Weyl's action. Relation between gauge transformations and diffeomorphisms. Spinors on curved manifolds. Minimally coupled Fermionic matter. Dirac Lagrangian.

§V. Maximally symmetric spaces

Homogeneous and isotropic spaces. Characterisation of maximally symmetric spaces: curvature constant and signature. MSS as vacuum solutions to the EH equations with cosmological constant. Construction from embedding in (D+1) pseudo-Lorentzian spaces: metric and Christoffel coefficients.

§VI. The Schwarzschild black hole

Spherically symmetric spaces. The Schwarzschild solution. Birkhoff's theorem. Singularities, definitions and criteria: curvature singularites and geodesic incompleteness. Free-fall towards the horizon. The tortoise coordinate. Extension of a space-time. Eddington-Finkelstein coordinates. Event horizons, black holes and white holes. Kruskal-Szekeres coordinates. Maximal extension of the Schwarzschild solution. Kruskal's diagram and eternal black holes. (A)dS-Schwarzschild space-time.

§VII. More general black holes

Conformal diagrams. Event horizons. Reissner-Nordström and Kerr black holes. Black hole thermodynamics.

§VII. Gravitational energy

Conserved quantities in gauge theories: the example of Yang-Mills theory. Covariant conservation and ordinary conservation. Einstein-Hilbert equations for asymptotically flat metrics. Candidate for gravitational energy-momentum tensor. The superpotential. ADM energy and momentum. Example: ADM energy of the Schwarzschild solution. The positive-energy theorem (without proof). Generic background with Killing vectors. Quadrupole radiation.

§VIII. Asymptotic symmetries

General notion of asymptotic symmetry group. The example of Maxwell's theory in flat space. Covariant phase space formalism. Asymptotically flat spacetime and Bondi-van der Burg-Metzner-Sachs supertranslations. Applications: soft theorems and memory effects.

Note: some topics may be assigned as homework problems, as an alternative to the oral exam

-Carroll S, Spacetime and Geometry: An Introduction to General Relativity (Addison-Wesley 2014/Cambridge University Press, 2019)
-Weinberg S, Gravitation and Cosmology - principles and applications of the general theory of relativity, (John Wiley \& Sons, 1972)
-Wald R, General Relativity (The University of Chicago Press, 1984)

1st module program (6 credits)

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.
Curie-Weiss 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 Mermin-Wagner theorem.
Renormalization team.
Kadanoff-Wilson transformation.
Calculation of fixed points for the Landau-Wilson 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

1 - Review of Thermodynamics and Statistical Mechanics.
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 short-range 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 X-ray and neutron scattering techniques. Structure factors and radial distribution functions of liquid and liquid molecular mixtures. Classic density functional theory. Ornstein-Zernike equation.
Closing relations for the density functional.

3 - Numerical simulation of liquid and soft material

Stochastic and deterministic simulation methods. Molecular Dynamics Method. Verlet-style 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
Time-dependent 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. Fluctuation-dissipation 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.

Please refer to the page
https://www.uniroma3.it/insegnamento-erogato/dipartimento-di-scienze/l/2023-2024/scienze-biologiche-0580706201300001/d56a627b-e9f4-49f6-abf5-62de4a1de19e--20410003/
of the Degree Course in Biological Sciences, which offers the teaching of

Please refer to the page
https://www.uniroma3.it/insegnamento-erogato/dipartimento-di-scienze/l/2023-2024/scienze-biologiche-0580706201300001/d56a627b-e9f4-49f6-abf5-62de4a1de19e--20410003/
of the Degree Course in Biological Sciences, which offers the teaching of

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"

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/

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.

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 1 Program
Electronic properties of solids
Reminds on band structure calculation methods. Band structure of III-V and IV semiconductors. Band structures and Fermi surfaces of selected metals. Effective mass approximation. Impurity levels in doped semiconductors.
Transport properties
The Drude Model. Semiclassical equations of transport. Boltzmann equation. Electron phonon interaction. Relaxation time approximation. Electrical conductivity in the relaxation time approximation. Thermoelectric power and thermal conductivity. 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.

Optical properties
Maxwell Equations in solids. Complex Dielectric Constant. Absorption and reflection coefficients. Kramers Kronig Relations. Lorentz Oscillator. 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. Spontaneous and stimulated Emission, Photoluminescence, Electroluminesce, optical gain. Semiconductor diode laser.

Magnetic properties of matter.
Energy levels and density of states of a free electron gas in a magnetic field. Filling of Landau levels as a function of the magnetic field. Magneto-transport.
Quantum mechanical treatment of magnetic susceptibility. Pauli paramagnetism. Magnetic susceptibility of closed-shell systems. Permanent magnetic dipoles in atoms and ions with partially filled shells. Paramagnetism of localized magnetic moments. Curie law. Van Vleck paramagnetism, Pauli paramagnetism and Landau diamagnetism. Magnetic ordering in crystals. Mean field theory of ferromagnetism: Weiss model. Curie-Weiss law. Anti-Ferromagnetism. Exchange interaction and Heisemberg model. Microscopic origin of the coupling between localized magnetic moments. Dipolar interaction and magnetic domains.

Section 2- Program
Heterojunctions and heterostructures. 2, 1, -0 dimensional systems: electronic states and density of states. 2 dimensional electron gases. Characteristics lengths for the electrical transport in low dimensional systems. Resonant tunnel diode. Aharonov-Bohm effect. Balistic transport and conductance quantization in 1D systems. 2D gas in a magnetic field: Shuinikov-de-Haas oscillations and quantum Hall effect. Single electron tunneling and coulomb blockade effects. Single electron transistor. Semiconductor qu-bits for quantum computing (brief).
Optical properties of nanostructures: interband and intersubband transitions in quantum wells. Nanostructures for light-emitters: heterostructure LED and lasers, quantum cascade lasers (brief).

Ashcroft-Mermin: "Solid State Physics"
Grosso-Pastori-Parravicini: "Solid State Physics"
Datta s.: Electronic transport in mesoscopic systems [Cambridge university press ]
Davies j. H. : The physics of low dimensional semiconductors [Cambridge university press)

Section 1 Program
Electronic properties of solids
Reminds on band structure calculation methods. Band structure of III-V and IV semiconductors. Band structures and Fermi surfaces of selected metals. Effective mass approximation. Impurity levels in doped semiconductors.
Transport properties
The Drude Model. Semiclassical equations of transport. Boltzmann equation. Electron phonon interaction. Relaxation time approximation. Electrical conductivity in the relaxation time approximation. Thermoelectric power and thermal conductivity. 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.

Optical properties
Maxwell Equations in solids. Complex Dielectric Constant. Absorption and reflection coefficients. Kramers Kronig Relations. Lorentz Oscillator. 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. Spontaneous and stimulated Emission, Photoluminescence, Electroluminesce, optical gain. Semiconductor diode laser.

Magnetic properties of matter.
Energy levels and density of states of a free electron gas in a magnetic field. Filling of Landau levels as a function of the magnetic field. Magneto-transport.
Quantum mechanical treatment of magnetic susceptibility. Pauli paramagnetism. Magnetic susceptibility of closed-shell systems. Permanent magnetic dipoles in atoms and ions with partially filled shells. Paramagnetism of localized magnetic moments. Curie law. Van Vleck paramagnetism, Pauli paramagnetism and Landau diamagnetism. Magnetic ordering in crystals. Mean field theory of ferromagnetism: Weiss model. Curie-Weiss law. Anti-Ferromagnetism. Exchange interaction and Heisemberg model. Microscopic origin of the coupling between localized magnetic moments. Dipolar interaction and magnetic domains.

Section 2- Program
Heterojunctions and heterostructures. 2, 1, -0 dimensional systems: electronic states and density of states. 2 dimensional electron gases. Characteristics lengths for the electrical transport in low dimensional systems. Resonant tunnel diode. Aharonov-Bohm effect. Balistic transport and conductance quantization in 1D systems. 2D gas in a magnetic field: Shuinikov-de-Haas oscillations and quantum Hall effect. Single electron tunneling and coulomb blockade effects. Single electron transistor. Semiconductor qu-bits for quantum computing (brief).
Optical properties of nanostructures: interband and intersubband transitions in quantum wells. Nanostructures for light-emitters: heterostructure LED and lasers, quantum cascade lasers (brief).

Ashcroft-Mermin: "Solid State Physics"
Grosso-Pastori-Parravicini: "Solid State Physics"
Datta s.: Electronic transport in mesoscopic systems [Cambridge university press ]
Davies j. H. : The physics of low dimensional semiconductors [Cambridge university press)

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

- 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.

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.
Interpretation of photoemission spectra. Koopmans' theorem, satellite peaks, limit of interrpetazione to independent particles. Many-body effects. Chemical shift (Lu 6.3.5, Hu 1.4,1.5,2.1,2.2) Photoemission in solids, the three-step model. Examples of applications.

Reverse photoemission (outline) (Lu 6.3, for further information Hu 6) Photoemission resolved in the corner. Valence photoemission and band structure. Photoemission of cores, photoelectrondiffraction. Examples of applications (Lu 6 and Panel XI, Hu 7.1, 7.2, 7.3.1) Outline of scanning probe microscopy (STM, AFM, SNOM) (Lu Panel VI and notes)

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"

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/

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.

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

(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

(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

COURSE CONTENT
Lessons (2CFU):
Introduction to particle detectors (scintillators, gaseous chambers, solid state)
Introduction to electronic devices for particle physics
Basic software development for DAQ system and data analysis

Lab Activity (6CFU):
Measurement of the Muon life

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

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

RECOMMENDED TEXTS:
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