Physics | University of Parma

Professor
Academic discipline: Fisica teorica, modelli e metodi matematici (FIS/02)
Field: Teorico e dei fondamenti della fisica
Type of training activity: Characterising

48 hours
of face-to-face activities

6 credits

hub:

course unit
in - - -

lectures timetable unavailable

exam calls

Learning objectives

The main theme of
this course is the idea of renormalization to gauge theories.

Prerequisites

Teoria dei campi

Course unit content

This course includes path integral quantization,
renormalization of non-Abelian gauge theories, spontaneous symmetry breaking. The goal is to compute the
beta function in on-Abelian gauge theories and discuss asymptotic freedom.

Full programme

Functional methods Path integrals in quantum mechanics and quantum field theory.Perturbation theory and Feynman
diagrams.Feynman rules from path integrals.Fermions and Grassman variables.
Renormalisation Ultraviolet divergences and regularisation. Dimensional regularisation.Renormalised perturbation theory.
Renormalisation group. Renormalization conditionBeta functions and anomalous dimensions, IR/UV fixed points, Callan-
Symanzik equation.1PI effective action. Derivative expansion of 1PI effective action; Effective potential. Spontaneous
symmetry breaking, Nambu-Goldstone theorem - proof by 1PI effective action and Ward identity.
Non-Abelian gauge field theory Abelian and non-Abelian gauge symmetries.QCD and Yang-Mills theory.Gauge fixing
and Faddeev-Popov ghosts.Computation of the beta function.Asymptotic freedom, colour confinement and the continuum
limit.

Bibliography

C. Itzykson, C. Zuber ‘‘Quantun field theory’, McGrow-Hill ed.
M.Peskin, D Schroeder, ‘‘An Introduction to quantum filed theory’, Addison Welsey ed.

Teaching methods

Oral lesson

Assessment methods and criteria

homeworks, final written exam, seminar on a particular subject

Other information

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QUANTUM THEORY OF GAUGE FIELDS cod. 1001052