Unruh-DeWitt Detector Response in Toroidal Spacetime

TL;DR

This paper investigates how an Unruh-DeWitt detector can detect the global topology of spacetime, specifically in a Minkowski spacetime with toroidal compactification, through different types of acceleration trajectories.

Contribution

It demonstrates that local quantum measurements via particle detectors can reveal large-scale topological features of spacetime, which are otherwise invisible to local curvature measurements.

Findings

Detector transition rates vary with topology and trajectory.

Inertial and accelerated detectors show distinct signatures of the toroidal topology.

Local measurements can detect global spatial features of spacetime.

Abstract

The global topology of spacetime, though invisible to local curvature measurements, leaves signatures on the correlation functions of quantum fields. We study these signatures using an Unruh-DeWitt particle detector operating in four-dimensional Minkowski spacetime with two spatial directions periodically identified, yielding a spatial topology $\mathbb{R}\times T^2$. We compute detector transition rates for three trajectories: uniform inertial motion, uniform proper acceleration directed along one of the compact axes, and uniform proper acceleration along the non-compact axis. Our results show how a local quantum measurement can reveal features of the large-scale spatial topology.