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.

Symmetries and conservation laws, continuous and discrete trasforms, parity, charge conjugation, time reversal. Relativistic quantum equations, Klein-Gordon equation, Dirac equation, negative Energy solutions, helicity, non-relativistic limit, the spin, anti-particles. Solutions for zero mass, properties of neutrinos.
Relativistic perturbation theory, quantum electrodynamics, Feynman diagrams, the propagator. Relativistic expression of Rutherford cross section, Mott, Dirac and Rosenbluth cross section.
Cosmic rays, primary and secondary components, discovery of mesons. Properties of muon and pion, strange particles, isospin Multiplets. Elementary particles and fundamental interactions, leptons and hadrons, mesons and baryons, anti-particles.
Hadronic interactions, isospin, the Yukawa model, pion-nucleon elastic scattering, the Delta resonance, baryonic and mesonic resonances, meson and baryon multiplets. Unitary symmetries, SU(2), SU(3), static quark model, u-d-s quarks, representation of baryons and mesons, magnetic moment of baryons, the colour of quarks.
Weak interactions, nuclear beta decay, Fermi and Gamow-Teller transitions, parity non-conservation, beta decay of polarized Co60. Helicity of the neutrino, V-A interaction. Muon decay, the Fermi constant. Pion decay, production of neutrino beams, leptonic number conservation, the two neutrinos e/mu. Neutrino interactions, the weak interaction propagator.
Particle decays in the quark model, weak decays of strange particles, the Cabibbo angle. K0 mesons, CP eigenstates, K0L and K0S mesons, the Glashow-Iliopoulos-Maiani hypothesis and the charm quark. CP-symmetry violation, the Cabibbo-Kobayashi-Maskawa miixing matrix and the beauty quark.
Inelastic lepton-nucleon scattering, struccature functions, Bjorken scaling, the parton model, parton densities, Inelastic neutrino and anti-neutrino scattering, quark and anti-quark densities, the gluons.
Electron-positron interaction, scattering and annihilation, hadron production, quarkonium, the tau lepton, production of heavy quarks.
Particle production in hadronic interactions, Drell-Yan processes, hadronic jets, quantum chromodynamics.
The top quark, the tau neutrino, the three generations.
Weak isospin and weak hypercharge, the Glashow-Weinberg-Salam model, electro-weak unification, discovery of W and Z bosons. Electro-weak symmetry breaking, the Higgs field, discovery of the Higgs boson.

• Quarks and Leptons, F. Halzen and A.D Martin, Quarks and Leptons, °An Introductory Course in Modern Particle Physics°, ISBN-10: 8126516569
ISBN-13: 978-8126516568
• Notes
http://webusers.fis.uniroma3.it/~ceradini/efns.html

Symmetries and conservation laws, continuous and discrete trasforms, parity, charge conjugation,
time reversal. Relativistic quantum equations, Klein-Gordon equation, Dirac equation, negative
Energy solutions, helicity, non-relativistic limit, the spin, anti-particles. Solutions for zero mass,
properties of neutrinos.
Relativistic perturbation theory, quantum electrodynamics, Feynman diagrams, the propagator.
Relativistic expression of Rutherford cross section, Mott, Dirac and Rosenbluth cross section.
Cosmic rays, primary and secondary components, discovery of mesons. Properties of muon and
pion, strange particles, isospin multiplets. Elementary particles and fundamental interactions,
leptons and hadrons, mesons and baryons, anti-particles.
Hadronic interactions, isospin, the Yukawa model, pion-nucleon elastic scattering, the Delta
resonance, baryonic and mesonic resonances, meson and baryon multiplets. Unitary symmetries,
SU(2), SU(3), static quark model, u-d-s quarks, representation of baryons and mesons, magnetic
moment of baryons, the colour of quarks.
Weak interactions, nuclear beta decay, Fermi and Gamow-Teller transitions, parity nonconservation, beta decay of polarized Co60. Helicity of the neutrino, V-A interaction. Muon
decay, the Fermi constant. Pion decay, production of neutrino beams, leptonic number
conservation, the two neutrinos e/mu. Neutrino interactions, the weak interaction propagator.
Particle decays in the quark model, weak decays of strange particles, the Cabibbo angle. K0
mesons, CP eigenstates, K0L and K0S mesons, the Glashow-Iliopoulos-Maiani hypothesis and
the charm quark. CP-symmetry violation, the Cabibbo-Kobayashi-Maskawa miixing matrix and
the beauty quark.
Inelastic lepton-nucleon scattering, struccature functions, Bjorken scaling, the parton model,
parton densities, Inelastic neutrino and anti-neutrino scattering, quark and anti-quark densities,
the gluons.
Electron-positron interaction, scattering and annihilation, hadron production, quarkonium, the tau
lepton, production of heavy quarks.
Particle production in hadronic interactions, Drell-Yan processes, hadronic jets, quantum
chromodynamics. The top quark, the tau neutrino, the three generations.
Weak isospin and weak hypercharge, the Glashow-Weinberg-Salam model, electro-weak
unification, discovery of W and Z bosons. Electro-weak symmetry breaking, the Higgs field,
discovery of the Higgs boson.

• W. E. Burcham and M. Jobes, Nuclear and Particle Physics, Pearson Education.
• Appunti del corso di Istituzioni di Fisica Nucleare e Subnucleare,
http://webusers.fis.uniroma3.it/~ceradini/efns.html

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.

TESTO PRINCIPALE:
Giuseppe Grosso and Giuseppe Pastori Parravicini Solid State Physics Academic Press

ALTRI TESTI UTILIZZATI:
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

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

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

Gravity
The Earth’s size and shape.
Gravitation.
The Earth’s rotation.
The Earth’s figure and gravity.
Gravity anomalies.
Interpretation of gravity anomalies.
Isostasy.
Rheology.

Seismology
Elasticity theory.
Seismic waves.
Earthquake seismology.
Seismic wave propagation.
Internal structure of the Earth.

Earth’s age and thermal properties
Geochronology.
The Earth’s heat.

Geomagnetism and paleomagnetism
The Physics of magnetism.
Rock magnetism.
Geomagnetism.
Paleomagnetism.

Fundamentals of Geophysical Fluid Dynamics
Time derivatives for fluids.
The mass continuity equation.
The momentum equation.
The equation of state.
Thermodynamic relations.
Thermodynamic equation for fluids.
Compressible and incompressible flow.
The energy budget.

Physics of the Atmosphere
Heterogeneous systems.
Transformations of moist air.
Hydrostatic equilibrium.
Static stability.
Radiative transfer.
Large-scale motion.
Wave propagation.
The general circulation.
Dynamic stability.

Physics of the Ocean
Oceans and Seas.
Atmospheric influences.
The oceanic heat budget.
Wind driven ocean circulation.
Deep circulation in the ocean.
Equatorial processes.
Ocean waves.
Coastal processes and tides.

Stacey F.D. and Davis P.M. - Physics of the Earth. Cambridge University Press, 2008 - ISBN:9780521873628

Vallis G.K. - Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, 2006 - ISBN:9780521849692

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

- 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]

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.

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. 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. Electron phonon interaction. Matrix elements and selection rules.

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.

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"

Ist Part

1 - Characterization of the states of matter. Ordered and disordered structures. Classical and quantum limit for atomic systems.
Examples of phase diagrams: argon, H2O, He4. Density correlation function and two particle distribution function. Examples of structure of some liquids

2 - Homogeneous electron gas in a neutralizing background (jellium model).
Zero order approximation: Sommerfeld theory. Coulombian interaction as perturbation. Hartree-Fock theory for electron gas. Distribution function for electron gas. Definition of correlation energy.

3 - The Green Functions for the Electron Gas. Green functions for non-interacting electrons. Lehmann representation.
Perturbative development for Green's functions. Dyson equation. Self-energy.

4 - Polarization propagator. Polarization diagrams. Proper polarization.
Correlation energy in terms of polarization propagator. Random phase approximation (RPA). Dielectric function in RPA. High-density limit, Thomas-Fermi screen. Limit to large wavelengths, plasma oscillations.

2nd Part

1 - The phenomenon of superfluity. The phase diagram of He4. The superfluid phase of liquid helium.
The theory of the two fluids. Landau's theory: critical speed, rotons and phonons.
Bogoliubov's theory of interacting bosons.
Hydrodynamics and vorticity. Vortices as liquid helium excitations.
Recent achievements of Bose-Einstein condensation.

2 - The phenomenon of superconductivity. Zero resistance, Meissner Effect, Critical Magnetic Field,
Specific heat. Analogies with the phenomenon of superfluidity. London equation. Thermodynamic considerations.
Superconductors of the first type and of the second type.

3 - Microscopic theory of superconductivity. Electron-phonon interaction. Attractive interaction between electrons. Cooper pairs. Bardeen-Cooper-Schrieffer's theory (BCS): fundamental state, definition of energy gap. Excited states. Calculation at finite temperature. Quantization of magnetic flux.

4 - Phenomenological theory of Ginzburg-Landau. Landau theory of phase transitions. Free energy of superconductors.
Ginzburg-Landau equations and relation with the London equation. Symmetry breaking and transition from normal to superconducting state.

A.L.FETTER, J.D.WALECKA "QUANTUM THEORY OF MANY PARTICLES"
G.GROSSO, G.PASTORI-PARRAVICINI "SOLID STATE PHYSICS"

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)

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 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
- Dalitz plots and their interpretation
- Quark model, mentions
- Parton model, quark and anti-quark density

c) Electro-weak interactions, decays, flavour mixing
- Hamiltonian and phenomenology of weak interazions. Cabibbo angle, GIM mechanism. Discovery of the charm quark and tau lepton.
- Standard model of electro-weak interactions and their experimental confirmations: discovery of neutral currents, W and Z bosons
- CP violation, meson mixing
- 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

e) Intro to experimental tools, also useful for theorists
- Radiation - matter interactions. Basics of particle detection techniques

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

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

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

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

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

- 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]

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

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 (EQUIVALENT TO APPROXIMATELY 2
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 6-7 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