Deligne-beilinson cohomology and Abelian link invariants

Abstract

For the Abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and we derive the main properties of the observables in a generic closed orientable 3-manifold. We present an explicit pathintegral non-perturbative computation of the Chern-Simons link invariants in the case of the torsion-free 3-manifolds S3, S1 × S2 and S1 × σg.