Unruh-DeWitt Fermion Detector on a (1+1)-Dimensional Cylindrical Spacetime: Arbitrary Worldlines and Inequivalent Spin Structures

TL;DR

This paper analyzes how an Unruh-DeWitt fermion detector responds to a massless Dirac field on a (1+1)-dimensional cylindrical spacetime, revealing sensitivity to spin structures and zero modes for arbitrary detector trajectories.

Contribution

It demonstrates the detector's ability to distinguish spin structures and accounts for zero mode contributions in a general setting with arbitrary motion.

Findings

Detector response differs for periodic and antiperiodic spin structures.

Zero mode contributes a state-dependent response.

Response is well-defined and controllable despite zero mode presence.

Abstract

We examine an Unruh-DeWitt particle detector which couples linearly to the scalar density of a massless Dirac field on the static cylindrical quotient of the (1+1)-dimensional Minkowski spacetime, allowing the detector's motion to remain arbitrary and working to leading order in perturbation theory. We show that the detector's response distinguishes the periodic and antiperiodic spin structures, and the zero mode that is present for periodic spinors contributes to the response by a state-dependent but well defined and controllable amount.