Exact QED Path Integration of the Maxwell Action, with Gravitational Curvature and Boundary Terms, Using Pontryagin Duality

TL;DR

This paper presents an exact method for calculating the QED path integral in curved spacetime using Pontryagin duality, revealing connections to gauge symmetry and non-Abelian gauge theories.

Contribution

It introduces a novel exact calculation technique for QED path integrals in curved spacetime incorporating boundary terms, leveraging Pontryagin duality and gauge symmetry.

Findings

Exact QED path integrals computed in curved spacetime.

Demonstration of gauge symmetry facilitating harmonic analysis.

Emergence of non-Abelian Yang-Mills theories from the analysis.

Abstract

We demonstrate how to explicitly calculate the QED path integral and associated Green functions, exactly, in curved spacetime, with retention of the boundary terms, to infinite order, for any and all spacetime manifolds with sufficient symmetry to admit the application of Pontryagin duality as a form of harmonic analysis. In the process we show how gauge symmetry itself greatly facilitates the ability to conduct harmonic analysis in curved spacetime and to do exact calculations with Pontryagin duality. We also show how non-Abelian, Yang-Mills gauge theories emerge naturally, if somewhat surprisingly, from this analysis.