Unruh-DeWitt Detector Response in Toroidal Spacetime
Nirmalya Kajuri, Sheeshram Siddh
TLDR
This paper shows how Unruh-DeWitt detectors can reveal global spacetime topology in a toroidal spacetime by measuring quantum field correlations.
Key contributions
- Studies Unruh-DeWitt detector response in 4D Minkowski spacetime with R x T^2 topology.
- Computes detector transition rates for three distinct trajectories.
- Demonstrates how local quantum measurements can reveal global spatial topology.
Why it matters
This work demonstrates a novel method to probe global spacetime topology using local quantum measurements. It's significant for understanding the interplay between quantum fields and spacetime structure, offering insights into quantum gravity and cosmology.
Original 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.
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