“Massless” vector field in de Sitter universe

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.

The Nature of Λ and the Mass of the Graviton: A Critical View

“…First, it is the only one among all non massless dS representations for which the Garidi mass vanishes, and it is part of an indecomposable structure issued from the existence of (constant) gauge solutions to (9.69). Secondly, it has been playing a crucial role in inflation theories, it is part of the Gupta-Bleuler structure for the massless spin 1 dS field (de Sitter QED) described by the UIR's Π + 1,1 [24], and it is the elementary brick for the construction of the massless spin 2 dS fields (de Sitter linear gravity) described by the UIR's Π + 2,2 [25]. Finally, the corresponding covariant quantum field theory requires a specific treatment due precisely to its indecomposable nature [26].…”

Conformally covariant vector–spinor field in de Sitter space

“…There exists another first-order field equation [8]: 24) which is invariant under the gauge transformation α →…”

“…There are two Casimir operators in the dS group and it has been shown that the massive scalar, vector, and spin-2 fields can be associated with the UIRs of the dS group [5,[20][21][22][23]. The massless fields can be associated with an indecomposable representation of the dS group [24]. The covariant quantum field theory for massive and massless conformally coupled scalar field in dS space have been studied in [5,25] and also for the massless minimally coupled scalar field in [26].…”

Linear Weyl gravity in de Sitter universe

“…In this notation, the relationship with UIRs of the dS group becomes straightforward because the Casimir operators are easily identified with the field equation [11]. The transverse tensor field K αβ (x) is locally determined by the "intrinsic" field h µν (X) through…”