A Class of Topological Actions

TL;DR

This paper reviews generalized parallel transports using Cheeger-Simons differential characters and Deligne-Beilinson cohomology, extending to distributions for quantized fields, providing a mathematical framework for topological actions.

Contribution

It introduces a unified mathematical framework for topological actions using advanced cohomology theories and extends the concept of parallel transport to distributions.

Findings

Provides integration formulas in Deligne-Beilinson cohomology

Extends parallel transport to distributions in quantized fields

Offers a comprehensive review of topological actions

Abstract

We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be extended to situations involving distributions as is appropriate in the context of quantized fields.