The Unruh Effect in General Boundary Quantum Field Theory

TL;DR

This paper explores the Unruh effect within the general boundary formulation of quantum field theory, analyzing expectation values of local observables and the impact of different quantization methods on their coincidence.

Contribution

It demonstrates the coincidence of expectation values in the GBF framework using Feynman quantization and highlights the failure of this coincidence under Berezin-Toeplitz quantization.

Findings

Coincidence of expectation values in Minkowski vacuum and Rindler space with Feynman quantization

Failure of expectation value coincidence with Berezin-Toeplitz quantization

Discussion of challenges in identifying the Minkowski vacuum as a thermal state in GBF

Abstract

In the framework of the general boundary formulation (GBF) of scalar quantum field theory we obtain a coincidence of expectation values of local observables in the Minkowski vacuum and in a particular state in Rindler space. This coincidence could be seen as a consequence of the identification of the Minkowski vacuum as a thermal state in Rindler space usually associated with the Unruh effect. However, we underline the difficulty in making this identification in the GBF. Beside the Feynman quantization prescription for observables that we use to derive the coincidence of expectation values, we investigate an alternative quantization prescription called Berezin-Toeplitz quantization prescription, and we find that the coincidence of expectation values does not exist for the latter.