A Class of Topological Actions
M. Bauer, G. Girardi, R. Stora, F. Thuillier

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.
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