Scheda programma d'esame
QUANTUM FIELDS AND TOPOLOGY
ENORE GUADAGNINI
Anno accademico2020/21
CdSFISICA
Codice328BB
CFU6
PeriodoSecondo semestre
LinguaItaliano

ModuliSettore/iTipoOreDocente/i
QUANTUM FIELDS AND TOPOLOGYFIS/02LEZIONI36
ENORE GUADAGNINI unimap
Obiettivi di apprendimento
Conoscenze

By the end of the course, the students will have acquired knowledge on 

general methods of quantization of gauge theories and of the so-called topological field theories, Chern-Simons and BF theories; 

basic notions of low dimensional topology: manifolds, knots and links, homotopy equivalence, ambient isotopy equivalence;

polynomial invariants of links, framed links, use of the skein relation, Alexander-Conway, Jones and  HOMFLY polynomials, linking number and related Gauss integral, fundamental group of a manifold and of the complement of a link, Seifert surface, surgery on three manifolds and the  Lickorish fundamental theorem;

solution of the abelian Chern-Simons theory in a generic 3-manifold.   

 

 

Modalità di verifica delle conoscenze

Presentation of a specific argument by the student, 

final oral examination

Capacità

perturbative computations in field theory, determination of the link polynomials, computations of the fundamental group

Modalità di verifica delle capacità

the student provides a presentation of a specific argument discussed in the course

Prerequisiti (conoscenze iniziali)

basic notions of quantum field theory

Syllabus

General aspects of perturbative quantum field theory (QFT). Example of cross section computation. Generating functionals in QFT. Action of Chern-Simons for abelian and non-abelian theories. General covariance, BRS gauge fixing, derivation of the Feynman propagator, Gauss linking number, gauge invariance, Wess-Zumino term. Basic definitions of knot theory, link poynomials, framed links. Gauge variables, holonomy, Wilson line operators. CS expectation values of holonomies associated with links. Skein relation, abelian and non-abelian link invariants obtained in the CS theory.   Surgery on 3-manifolds. 

Ultimo aggiornamento 11/09/2020 17:57