Photon propagator in de Sitter space in the general covariant gauge

TL;DR

This paper derives the photon propagator in de Sitter space within a general covariant gauge, revealing that de Sitter symmetry is broken except in the transverse gauge, which has implications for quantum field theory in curved spacetime.

Contribution

The authors construct the photon propagator in de Sitter space in a general covariant gauge using canonical quantization, providing a covariant position space form that clarifies symmetry properties.

Findings

Photon propagator breaks de Sitter symmetry in general covariant gauges.

Symmetry is preserved only in the transverse gauge.

Derived the propagator as a sum-over-modes in momentum space.

Abstract

We consider a free photon field in $D$-dimensional de Sitter space, and construct its propagator in the general covariant gauge. Canonical quantization is employed to define the system starting from the classical theory. This guarantees that the propagator satisfies both the equation of motion and subsidiary conditions descending from gauge invariance and gauge fixing. We first construct the propagator as a sum-over-modes in momentum space, carefully accounting for symmetry properties of the state. We then derive the position space propagator in a covariant representation, that is our main result. Our conclusions disagree with previous results as we find that the position space photon propagator necessarily breaks de Sitter symmetry, except in the exact transverse gauge limit.