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

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