Università degli Studi di Perugia

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Study-unit Code
In all curricula
Maria Cristina Diamantini
Course Regulation
Coorte 2018
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa integrata


Code GP005492
Teacher Maria Cristina Diamantini
  • Maria Cristina Diamantini - Didattica Ufficiale
  • 42 ore - Didattica Ufficiale - Maria Cristina Diamantini
Learning activities Caratterizzante
Area Teorico e dei fondamenti della fisica
Sector FIS/02
Type of study-unit Obbligatorio (Required)
Language of instruction Italian
Discrete Symmetries in quantum mechanics.
Relativistic quantum mechanics: Klein-Gordon and Dirac equations.
Solutions of the free Dirac equation.
Relativistic hydrogen atom.
Reference texts
Sakurai, Modern quantum mechanics.
Itzykson-Zuber, Quantum Field Theory.
Educational objectives
Aim of the course is the introduction to relativistic quantum mechanics, negative energy solutions and use of Dirac matrices.
Knowledges of quantum mechanics and special relativity
Teaching methods
Theory courses
Other information
Learning verification modality
Exercises sessions to verify comprehension.
Extended program
Discrete symmetries in quantum mechanics.Parity. Anti-unitary 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.


Code GP005493
CFU 10
Teacher Gianluca Grignani
  • Gianluca Grignani - Didattica Ufficiale
  • 70 ore - Didattica Ufficiale - Gianluca Grignani
Learning activities Caratterizzante
Area Teorico e dei fondamenti della fisica
Sector FIS/02
Type of study-unit 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 (tree-level) amplitudes of quantum electrodynamics processes.
Prerequisites In order to be able to understand the arguments treated in the course an in-depth 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; Klein-Gordon equation; problems in the single particle interpretation; Dirac equation; particles e anti-particles. motivation to quantum field theory. Classical field theory: Lagrangian formulation; Lorentz invariance and locality. Noether theorem.
Quantization of free fields
Real scalar field: Klein-Gordon 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. Plane-wave solution of the free Dirac equation; anti-commutation rules; Fock space and Fermi-Dirac statistic. Fermionic Feynman propagator.
Electromagnetic field: Maxwell equations and action principle; gauge symmetry. Covariant quantization of the e.m. field; Gupta-Bleuler 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: electron-positron annihilation and creation of muon-antimuon; electron scattering; electron-positron annihilation; Bhabha scattering; Compton scattering.
Hint of radiative corrections and renormalization
Källén-Lehmann spectral representation. Mass and charge renormalization in QED.
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