The course is dedicated to present the main properties of certain quantum field theories in which the observables are related with topological invariants of low dimensional topology. The considered models are the abelian and non-abelian Chern-Simons quantum field theories together with the so-called BF model, which are defined in three dimensions. The basic definitions of gauge quantum field theories are recalled in the first part of the course; then, the lagrangian density and the perturbative setting of the Chern-Sions theory are described. The properties of the observables associated with framed knots and links are worked out. The basic definitions of knot theory are recalled, and the computation of the link polynomials is discussed. The complete solution of the abelian Chern-Simons theory in a generic 3-manifold is discussed. The perturbative computations in the non-abelian case and in the BF model are presented.
- Teacher: ENORE GUADAGNINI