CORSI
Introduzione ai Metodi funzionali e Teorie di Gauge
Introduction to Functional Methods and Gauge Theories
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Durata
36 ore
Lingua
Inglese
Sede didattica
Scuola Superiore Catania
Coordinatore/proponente
Alfio Bonanno
(INAF, Catania)
Vincenzo Damiani
(Università di Catania)
Docente
Alfio Bonanno
(INAF, Catania)
Calendario
- 12 maggio, 15.00-18.00
- 13 maggio, 17:00-21:00
- 14 maggio, 17.00-21.00
- 15 maggio, 18.00-21.00
- 16 maggio, 17.00-21.00
- 17 maggio, 08:30-10.30
- 26 maggio, 17:00–21:00
- 27 maggio, 17:00–21:00
- 28 maggio, 17:00–21:00
- 29 maggio, 19:00–21:00
- 30 maggio, 19:00–21:00
Docente
Dario Zappalà
(INFN, Catania)
Calendario
- 12 maggio, 15.00-18.00
- 13 maggio, 17:00-21:00
- 14 maggio, 17.00-21.00
- 15 maggio, 18.00-21.00
- 16 maggio, 17.00-21.00
- 17 maggio, 08:30-10.30
- 26 maggio, 17:00–21:00
- 27 maggio, 17:00–21:00
- 28 maggio, 17:00–21:00
- 29 maggio, 19:00–21:00
- 30 maggio, 19:00–21:00
Obiettivi formativi
The course will provide a general introduction to the physics of functional integral and gauge theories, starting from essential notions and covering various aspects of the subject, ranging from the main properties of quantum electrodynamics to the more complex Yang-Mills theories. The general aim is to provide the students with the fundamental theoretical elements necessary to achieve a basic understanding of, at least, some of the many contexts where gauge theories play a central role, such as the electroweak and/or strong interactions, or even the gravitational interactions.
Contenuti del corso
Part I
Reminder about Lorentz and Translational Invariance in Field Theory The canonical energy-momentum and angular momentum densities The canonical momentum and angular momentum Angular momentum in a relativistic theory Lorentz transformation properties of the gauge field Aµ(x) and its consequences Quantization of a gauge theory Problems in the quantization procedure in Gauge Theories Gauge invariance vs. gauge independence The Dirac method for constrained systems Dirac method and Dirac bracket First class vs second class constraints Particle moving on a sphere Relativistic particle Dirac Field Theory Maxwell Field Theory.
Part II
Path Integral quantization; Yang-Mills theories quantization, gauge fixing and Faddeev-Popov ghosts; Quantum electrodynamics (QED) and Ward identities, Renormalization of QED; Yang Mills BRST symmetry and Slavnov-Taylor identities; Beta function, Landau pole of QED, asymptotic freedom of Yang- Mills theory
Metodologia didattica
The teaching consists of frontal lectures, which contain a part of exercise.
Modalità della verifica finale di apprendimento
The final exam consists of an oral scrutiny with questions covering the whole subject treated in the lectures.
Calendario programmato
II Semestre (da marzo/aprile a settembre 2026).
Eventuali prerequisiti degli/lle allievi/e frequentanti
Quantum Mechanics.
