Conformally covariant quantization of Maxwell field in de Sitter space

TL;DR

This paper presents a conformally invariant quantization of the Maxwell field in de Sitter space, resulting in a new simple two-point function and utilizing a geometric approach combined with Gupta-Bleuler quantization.

Contribution

It introduces a novel de Sitter invariant two-point function for the Maxwell field using a geometric realization and a canonical Gupta-Bleuler quantization scheme.

Findings

Derived a new simple de Sitter invariant two-point function.

Established invariance under SO(2,4) and de Sitter groups.

Applied a geometric approach to field quantization.

Abstract

In this article, we quantize the Maxwell ("massless spin one") de Sitter field in a conformally invariant gauge. This quantization is invariant under the SO$_0(2,4)$ group and consequently under the de Sitter group. We obtain a new de Sitter invariant two-points function which is very simple. Our method relies on the one hand on a geometrical point of view which uses the realization of Minkowski, de Sitter and anti-de Sitter spaces as intersections of the null cone in $\setR^6$ and a moving plane, and on the other hand on a canonical quantization scheme of the Gupta-Bleuler type.