Gupta-Bleuler quantization for minimally coupled scalar fields in de Sitter space

TL;DR

This paper develops a covariant quantization method for massless scalar fields in de Sitter space, avoiding infrared divergences by using a group-theoretical approach and Krein spaces, and clarifies the representation theory involved.

Contribution

It introduces a fully covariant quantization scheme for massless fields in de Sitter space using Krein spaces, linking the field theory to specific unitary representations of the de Sitter group.

Findings

The formalism is free of infrared divergences.

Negative norm modes do not lead to negative energies.

Explicit correspondence between de Sitter group representations and field theory.

Abstract

We present in this paper a fully covariant quantization of the minimally-coupled massless field on de Sitter space. We thus obtain a formalism free of any infrared (e.g logarithmic) divergence. Our method is based on a rigorous group theoretical approach combined with a suitable adaptation (Krein spaces) of the Wightman-G\"{a}rding axiomatic for massless fields (Gupta-Bleuler scheme). We make explicit the correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter space-time. The minimally-coupled massless field is associated with a representation which is the lowest term of the discrete series of unitary representations of the de Sitter group. In spite of the presence of negative norm modes in the theory, no negative energy can be measured: expressions as $\le n_{k_1}n_{k_2}...|T_{00}|n_{k_1}n_{k_2}...\re$ are always positive.