The U(1) BF functional measure and the Dirac distribution on the space of quantum fields

Abstract

In this article, we explain how the U(1) BF measure can be related to the Fourier transform of a Dirac distribution defined on the Z-module of quantum fields. Then, we revisit the U(1) BF partition function with the help of this Dirac distribution and finally shed light on a natural relation between the U(1) BF and Chern-Simons theories.