Response of a uniformly accelerated Unruh-DeWitt detector in polymer quantization

TL;DR

This paper investigates how polymer quantization, used in loop quantum gravity, affects the response of an accelerated Unruh-DeWitt detector, revealing a non-thermal spectrum due to a finite regularization parameter.

Contribution

It demonstrates that polymer quantization modifies the detector's response, producing a non-thermal spectrum, contrasting with the standard Fock space predictions.

Findings

Polymer quantization introduces a finite regulator value (~2.16).

The detector's spectrum becomes non-thermal under polymer quantization.

Response of a spatially smeared detector is also analyzed.

Abstract

If an Unruh-DeWitt detector moves with a uniform acceleration in Fock-space vacuum, then the transition rate of the detector is proportional to the thermal spectrum. It is well known that the transition rate of the detector crucially depends on the two-point function along the detectors trajectory and in order to compute it the standard "$i \epsilon$" regularization is used for Fock space. Numerically, we show here that the regulator $\epsilon$ is generic in polymer quantization, the quantization method used in \emph{loop quantum gravity} with a finite value $\epsilon \approx 2.16$, which leads to non-thermal spectrum for the uniformly accelerated detector. We also discuss the response of a spatially smeared detector.