Normalizing Fock space states in static spacetimes

TL;DR

This paper examines how different normalization schemes for Fock space states behave in curved spacetimes, revealing that unlike flat spacetime, normalization choices affect scattering process definitions.

Contribution

It highlights the impact of normalization schemes on quantum field theory in curved spacetimes, showing they are not equivalent as in flat spacetime, and provides an illustrative example.

Findings

Normalization schemes differ in curved spacetimes.

Scattering processes depend on the normalization scheme.

Wave packet and box normalization are equivalent in flat spacetime.

Abstract

In quantum field theory, sharp momentum states have to be normalized to be in Fock space. We investigate different normalization schemes, both box normalization and wave packets. These methods are equivalent in flat spacetimes, but turn out to produce different results in curved spacetimes, specifically in those that break translation invariance. This means that scattering processes have to be defined in relation to the normalization scheme used, rather than being independent of it as is the case in flat spacetime. We provide an illustrative example of this phenomenon.