  In recent work by the authors, a connection between Feynman's path integral
and Fourier integral operator $\zeta$-functions has been established as a means
of regularizing the vacuum expectation values in quantum field theories.
However, most explicit examples using this regularization technique to date, do
not consider gauge fields in detail. Here, we address this gap by looking at
some well-known physical examples of quantum fields from the Fourier integral
operator $\zeta$-function point of view.
