"Massless" spin-2 field in de Sitter space

TL;DR

This paper develops a covariant quantization framework for a massless spin-2 field in de Sitter space, ensuring gauge invariance and avoiding infrared divergences, with positive energy in physical states.

Contribution

It introduces a Gupta-Bleuler type quantization for massless spin-2 fields in de Sitter space, maintaining covariance and gauge invariance while handling negative norm states.

Findings

The quantization is de Sitter covariant and gauge-invariant.

Infrared divergences are avoided in this framework.

Energy remains positive in physical states.

Abstract

In this paper, admitting a de Sitter (dS)-invariant vacuum in an indefinite inner product space, we present a Gupta-Bleuler type setting for causal and full dS-covariant quantization of free "massless" spin-2 field in dS spacetime. The term "massless" stands for the fact that the field displays gauge and conformal invariance properties. In this construction, the field is defined rigorously as an operator-valued distribution. It is covariant in the usual strong sense: $\underline{U}_g \underline{{\cal{K}}} (X) \underline{U}_g^{-1} = \underline{{\cal{K}}} (g.X)$, for any $g$ in the dS group, where $\underline{U}$ is associated with the indecomposable representations of the dS group, $SO_0(1,4)$, on the space of states. The theory, therefore, does not suffer from infrared divergences. Despite the appearance of negative norm states in the theory, the energy operator is positive in all physical states and vanishes in the vacuum.