Violation of Kubo-Martin-Schwinger condition along a Rindler trajectory in polymer quantization

Abstract

Existence of Unruh effect is often understood from the property of two-point function along Rindler trajectory where it satisfies KMS condition. In particular, it exhibits the so-called KMS periodicity along imaginary time direction. Corresponding period is then identified with reciprocal of Unruh temperature times Boltzmann constant. We show here that the two-point function including leading order perturbative corrections due to polymer quantization, the quantization method used in loop quantum gravity, violates KMS condition in low-energy regime. This violation is caused by correction terms which are not Lorentz invariants. Consequently, polymer corrected two-point function along Rindler trajectory looses its thermal interpretation. We discuss its implications on existence of Unruh effect in the context of polymer quantization.