An extension of the U\!(1) 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.

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