Invariant quantization in warped spacetimes

TL;DR

This paper demonstrates that quantum theory in warped spacetimes can be made invariant under continuous spacetime symmetries connected to the identity, using a mode decomposition specific to warped geometries.

Contribution

It proves that invariance under continuous spacetime symmetries can be implemented in quantum theory on warped spacetimes at the first quantization level.

Findings

Invariance under continuous spacetime symmetries is achievable in warped spacetimes.

Mode decomposition tailored to warped spacetimes facilitates this invariance.

The approach is applicable at least at the first quantization level.

Abstract

We argue that quantum theory in curved spacetime should be invariant under the continuous spacetime symmetries thaat are connected with the identity. For typical warped-product spacetimes, we prove that such invariance can be actually implemented, at least at the level of first quantization. Our approach rests on a mode decomposition which is special to the context of warped spacetimes.