Exact Computations in Topological Abelian Chern-Simons and BF Theories

الملخص EN

We introduce Deligne cohomology that classifies U1 fibre bundles over 3 manifolds endowed with connections.

We show how the structure of Deligne cohomology classes provides a way to perform exact (nonperturbative) computations in U1 Chern-Simons theory (BF theory, resp.) at the level of functional integrals.

The partition functions (and observables) of these theories are strongly related to topological invariants well known to the mathematicians.