Massless spin-2 field in de Sitter space

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.