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

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.