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

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.