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

TL;DR

This paper demonstrates that polymer quantization leads to violations of the KMS condition along Rindler trajectories, challenging the thermal interpretation of the Unruh effect within loop quantum gravity frameworks.

Contribution

It shows that polymer quantization introduces non-Lorentz invariant corrections that violate the KMS condition, affecting the Unruh effect's validity in this context.

Findings

Polymer corrections violate KMS condition at low energies.

Two-point function loses thermal interpretation due to non-invariance.

Implications for the existence of Unruh effect 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.