Relativistic Gauge Conditions in Quantum Cosmology

TL;DR

This paper investigates the quantization of the electromagnetic field in quantum cosmology, focusing on gauge conditions, one-loop effects, and gauge invariance using zeta-function regularization.

Contribution

It provides a detailed analysis of relativistic gauge conditions and their impact on quantum amplitudes in quantum cosmology.

Findings

Identified a gauge condition with a diagonal operator matrix.

Compared mode-by-mode and covariant evaluations of quantum amplitudes.

Analyzed gauge invariance of perturbative quantum theory.

Abstract

This paper studies the quantization of the electromagnetic field on a flat Euclidean background with boundaries. One-loop scaling factors are evaluated for the one-boundary and two-boundary backgrounds. The mode-by-mode analysis of Faddeev-Popov quantum amplitudes is performed by using zeta-function regularization, and is compared with the space-time covariant evaluation of the same amplitudes. It is shown that a particular gauge condition exists for which the corresponding operator matrix acting on gauge modes is in diagonal form from the beginning. Moreover, various relativistic gauge conditions are studied in detail, to investigate the gauge invariance of the perturbative quantum theory.