ECTS - University of Pisa
| Modules | Area | Type | Hours | Teacher(s) | |
| QUANTUM FIELDS AND TOPOLOGY | FIS/02 | LEZIONI | 36 |
|
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.
Presentation of a specific argument by the student,
final oral examination
perturbative computations in field theory, determination of the link polynomials, computations of the fundamental group
the student provides a presentation of a specific argument discussed in the course
basic notions of quantum field theory
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.
