Response of the Unruh-DeWitt detector in flat spacetime with a compact dimension

TL;DR

This paper examines how the response of an Unruh-DeWitt detector varies in flat spacetime with a compact dimension, revealing inertial frame non-equivalence and effects of acceleration in different directions.

Contribution

It analyzes the detector's transition rates for various motions in a compactified flat spacetime, highlighting the impact of compact dimensions on inertial and accelerated frames.

Findings

Inertial frames are not equivalent in compactified spacetime.

Acceleration in compact directions affects detector response.

Transition rates depend on the detector's motion and switching function.

Abstract

In a flat spacetime with one spatial dimension compactified, inertial reference frames are not all equivalent, but there are the preferred ones. This paper investigates the nonequivalence of inertial frames and also that of uniformly accelerated frames in connection with the response of the Unruh-DeWitt detector coupled to a massless scalar field. The detector's transition rates of both excitation and de-excitation are studied in depth for three different cases: (i) the detector moving at an arbitrary constant velocity, (ii) moving with a constant acceleration in the compact direction, and (iii) moving with a constant acceleration in noncompact directions. The instantaneous transition rate in relation to the switching function is also taken into account.