Transient response from Unruh-DeWitt detector along Rindler trajectory in polymer quantization

Abstract: If an Unruh-DeWitt detector operates for an infinite proper time along the trajectory of a uniformly accelerated observer in Fock space then induced transition rate of the detector is proportional to Planck distribution. For a realistic detector which operates only for a finite period, the instantaneous transition rate contains both transient and non-transient terms. In particular, the non-transient term contains a residue evaluated at the pole of the two-point function. We show here by considering a massless scalar field that unlike in Fock quantization, the short-distance two-point function contains no pole in polymer quantization, the quantization techniques used in loop quantum gravity. Consequently, corresponding transition rate of the Unruh-DeWitt detector contains only transient terms. Thus, the result presented here provides an alternative evidence for absence of Unruh effect in polymer quantization which was shown earlier by the authors using methods of Bogoliubov transformation and Kubo-Martin-Schwinger condition.