  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.
