Field/source duality in topological field theories

TL;DR

This paper explores the duality between fields and sources in topological field theories, defining a class where both are de Rham cocycles and coupling is via cohomology isomorphism, with applications to physical examples.

Contribution

It introduces a new class of topological field theories characterized by field/source duality through cohomology isomorphisms, providing a deeper theoretical foundation.

Findings

Defines topological field theories with field/source duality

Establishes isomorphism between field and source cohomology spaces

Applies the framework to elementary physical examples

Abstract

The relationship between the sources of physical fields and the fields themselves is investigated with regard to the coupling of topological information between them. A class of field theories that we call topological field theories is defined such that both the field and its source represent de Rham cocycles in varying dimensions over complementary subspaces and the coupling of one to the other is by way of an isomorphism of the those cohomology spaces, which we refer to as field/source duality. The deeper basis for such an isomorphism is investigated and the process is described for various elementary physical examples of topological field theories.