Unit THEORETICAL PHYSICS
THEORETICAL PHYSICS PART 1
Code  GP005492 

CFU  6 
Teacher  Maria Cristina Diamantini 
Teachers 

Hours 

Learning activities  Caratterizzante 
Area  Teorico e dei fondamenti della fisica 
Sector  FIS/02 
Type of studyunit  Obbligatorio (Required) 
Language of instruction  Italian 
Contents  Discrete Symmetries in quantum mechanics. Relativistic quantum mechanics: KleinGordon and Dirac equations. Solutions of the free Dirac equation. Relativistic hydrogen atom. 
Reference texts  Sakurai, Modern quantum mechanics. ItzyksonZuber, Quantum Field Theory. 
Educational objectives  Aim of the course is the introduction to relativistic quantum mechanics, negative energy solutions and use of Dirac matrices. 
Prerequisites  Knowledges of quantum mechanics and special relativity 
Teaching methods  Theory courses 
Other information  None 
Learning verification modality  Exercises sessions to verify comprehension. 
Extended program  Discrete symmetries in quantum mechanics.Parity. Antiunitary operators, time reversal. Relativistic quantum mechanics, Klein Gordon and Dirac equations. Dirac equation: gamma matrices, covariance, bilinear forms. Solutions of the free Dirac equation. Energy projectors. Spin. Dirac sea, charge conjugation. Dirac equation in presence of an electromagnetic field, non relativistic limit. Hydrogen atom. 
THEORETICAL PHYSICS PART 2
Code  GP005493 

CFU  10 
Teacher  Gianluca Grignani 
Teachers 

Hours 

Learning activities  Caratterizzante 
Area  Teorico e dei fondamenti della fisica 
Sector  FIS/02 
Type of studyunit  Obbligatorio (Required) 
Language of instruction  Italian 
Contents  • Elements of group theory and representation theory; • Lorentz and Poincaré groups;¿ • Introduction to quantum field theory;¿ • Quantization of free fields (scalar, Dirac and gauge fields); • Interacting fields; • Quantum electrodynamics (QED); • Hint of radiative corrections and renormalization. 
Reference texts  For the Group Theory part:¿ • W.K. Tung, Group Theory in Physics¿ • G. Fonda, G. Ghirardi, Symmetry Principles in Quantum Physics • H. Georgi, Lie Algebras in Particle Physics For the Quantum Field Theory part:¿ • F. Mandl, G. Shaw, Quantum Field Theory ¿ • M. Peskin, D. Schroeder, An Introduction to Quantum Field Theory • L.H. Ryder, Quantum Field Theory • C. Itzykson, J.B. Zuber, Quantum Field Theory¿ • J. Bjorken, S. Drell, Relativistic Quantum Fields 
Educational objectives  The course aims to provide the students with the main notions of the quantum field theory formalism. The students should gain knowledge of the perturbative approach to study interacting field theories and of the diagrammatic picture given by Feynman diagrams. Using this approach they should be able to compute (treelevel) amplitudes of quantum electrodynamics processes. 
Prerequisites  In order to be able to understand the arguments treated in the course an indepth knowledge of Quantum mechanics and Special Relativity is needed. 
Teaching methods  The course is organized as follows: • Lectures on all the subjects of the course; • Assignments of problem sets to be made in preparation of the exam. 
Other information  None. 
Learning verification modality  The exam consists in an oral interview, about one hour long, aiming to assess the knowledge level and the understanding capabilities achieved by the student on the theoretical and methodological contents as indicated on the course program. 
Extended program  Elements of group theory Structure of groups; subgroups, classes and invariant subgroups; cosets and factor groups; homomorphisms and isomorphisms; direct product. Group representations; equivalent representations; unitary representations; reducible and irreducible representations. Topological groups and Lie groups; compactness; connected groups; universal covering; generators; Lie algebra; Casimir operators. Relevant exampls: SU(2); SO(3) and its universal covering. Lorentz and Poincaré groups Lorentz group: definition and classification of Lorentz transformations; restricted Lorentz group and its universal covering; spinorial representation; Lorentz algebra; Casimir; relevant representations: scalars, vectors, Weyl and Dirac spinors. Poincaré group: algebra and Casimir; unitary representations. Introduction to quantum field theory Relativistic quantum mechanics; KleinGordon equation; problems in the single particle interpretation; Dirac equation; particles e antiparticles. motivation to quantum field theory. Classical field theory: Lagrangian formulation; Lorentz invariance and locality. Noether theorem. Quantization of free fields Real scalar field: KleinGordon equation and action principle; expansion in normal modes. Quantization of the free real scalar field; creation and annihilation operators; normal product; Fock space. Complex scalar field. Scalar Feynman propagator. Spinorial Dirac field: action principle; Noether currents; discrete symmetries (CPT). Fierz transformations. Planewave solution of the free Dirac equation; anticommutation rules; Fock space and FermiDirac statistic. Fermionic Feynman propagator. Electromagnetic field: Maxwell equations and action principle; gauge symmetry. Covariant quantization of the e.m. field; GuptaBleuler condition; Fock space. Photon Feynman propagator. Interacting fields: Quantum electrodynamics (QED) Spinor quantum electrodynamics: minimal coupling and gauge. Interaction picture; S matrix. Wick theorem. Feynman diagrams. Feynman rules for QED. Elementary processes: electronpositron annihilation and creation of muonantimuon; electron scattering; electronpositron annihilation; Bhabha scattering; Compton scattering. Hint of radiative corrections and renormalization KällénLehmann spectral representation. Mass and charge renormalization in QED. 