Integrating Gauge Fields in the $\zeta$-formulation of Feynman's path integral

Understand

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.