Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime
Résumé
In a recent Letter, we have pointed out that the linearized Einstein gravity in de Sitter (dS) spacetime, besides the spacetime symmetries generated by the Killing vectors and the evident gauge symmetry, also possesses a hitherto “hidden” local (gaugelike) symmetry which becomes anomalous on the quantum level. This gaugelike anomaly makes the theory inconsistent and must be canceled at all costs. In this companion paper, we first review our argument and discuss it in more detail. We argue that the cancellation of this anomaly makes it impossible to preserve dS symmetry in linearized quantum gravity through the usual canonical quantization in a consistent manner. Then, demanding that all the classical symmetries to survive in the quantized theory, we set up a coordinate-independent formalism à la Gupta-Bleuler which allows for preserving the (manifest) dS covariance in the presence of the gauge and the gaugelike invariance of the theory. On this basis, considering a new representation of the canonical commutation relations, we present a graviton quantum field on dS space, transforming correctly under isometries, gauge transformations, and gaugelike transformations, which acts on a state space containing a vacuum invariant under all of them. Despite the appearance of negative norm states in this quantization scheme, the energy operator is positive in all physical states and vanishes in the vacuum.
Mots clés
String theory
quantum gravity
gauge/gravity duality
symmetry: space-time
symmetry: gauge
quantization: canonical
gravitation: linear
gravitation: field theory
quantum gravity: linear
transformation: gauge
space-time: de Sitter
energy: operator
vector: Killing
anomaly
commutation relations
covariance
isometry
graviton
general relativity
gravitation: weak field
operator: Casimir