An extension of the $\mathrm{U}\left(1\right)$ BF theory, Turaev-Viro invariant and Drinfeld center construction. Part I: Quantum fields, quantum currents and Pontryagin duality

Abstract

In this first of a series of articles dedicated to natural extensions of the U(1) BF theory, abelian Turaev-Viro (TV) construction and corresponding Drinfeld center construction for any closed oriented smooth manifolds, we present the mathematical background that will be used.

58 pages, 2 figures