The effect of curvature on local observables in quantum field theory

TL;DR

This paper investigates how spacetime curvature influences local measurements of a massless scalar quantum field, providing leading order corrections and applying these to particle detector models.

Contribution

It introduces a method to compute curvature-induced corrections to local field observables using Riemann normal coordinates and the Hadamard condition.

Findings

Curvature causes measurable corrections to field correlations.

The corrections are explicitly computed for massless scalar fields.

Application to particle detectors quantifies curvature effects in localized probes.

Abstract

We compute the leading order corrections to the expected value of the squared field amplitude of a massless real scalar quantum field due to curvature in a localized region of spacetime. We use Riemann normal coordinates to define localized field operators in a curved spacetime that are analogous to their flat space counterparts, and the Hadamard condition to find the leading order curvature corrections to the field correlations. We then apply our results to particle detector models, quantifying the effect of spacetime curvature in localized field probes.