"Massless" vector field in de Sitter Universe

TL;DR

This paper presents the covariant quantization of a massless vector field in de Sitter space, emphasizing gauge invariance, group representations, and the use of de Sitter waves for a consistent quantum field theory formulation.

Contribution

It introduces a gauge fixing and mode construction for massless vector fields in de Sitter space, utilizing indecomposable representations and analyticity conditions.

Findings

Quantization framework for massless vector fields in de Sitter space established.

Simplified Gupta-Bleuler structure derived for the gauge fixing.

Mode functions constructed using de Sitter waves with group-theoretical properties.

Abstract

In the present work the massless vector field in the de Sitter (dS) space has been quantized. "Massless" is used here by reference to conformal invariance and propagation on the dS light-cone whereas "massive" refers to those dS fields which contract at zero curvature unambiguously to massive fields in Minkowski space. Due to the gauge invariance of the massless vector field, its covariant quantization requires an indecomposable representation of the de Sitter group and an indefinite metric quantization. We will work with a specific gauge fixing which leads to the simplest one among all possible related Gupta-Bleuler structures. The field operator will be defined with the help of coordinate independent de Sitter waves (the modes) which are simple to manipulate and most adapted to group theoretical matters. The physical states characterized by the divergencelessness condition will for instance be easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemanian manifold for the modes and the two-point function.