Gauge-Averaging Functionals for Euclidean Maxwell Theory in the Presence of Boundaries

TL;DR

This paper analyzes the one-loop quantum amplitudes of Euclidean electromagnetism with boundary conditions on a 3-sphere, using zeta-function regularization to understand different gauge-fixing choices in bounded quantum field theories.

Contribution

It provides a detailed calculation of zeta values for various gauge-averaging functionals in Euclidean Maxwell theory with boundaries, enhancing understanding of gauge quantization methods.

Findings

Explicit expressions for contributions to zeta values from physical and gauge modes

Comparison of different gauge-averaging functionals

Insights into boundary effects on gauge field quantization

Abstract

This paper studies the one-loop expansion of the amplitudes of electromagnetism about flat Euclidean backgrounds bounded by a 3-sphere, recently considered in perturbative quantum cosmology, by using zeta-function regularization. For a specific choice of gauge-averaging functional, the contributions to the full zeta value owed to physical degrees of freedom, decoupled gauge mode, coupled gauge modes and Faddeev-Popov ghost field are derived in detail, and alternative choices for such a functional are also studied. This analysis enables one to get a better understanding of different quantization techniques for gauge fields and gravitation in the presence of boundaries.