Note on the Unruh Effect

TL;DR

This paper explores the mathematical representation of the Unruh effect, showing how a uniformly accelerated detector perceives vacuum as thermal radiation through a specific wave equation solution in two dimensions.

Contribution

It provides a new representation of wave solutions in Rindler regions, clarifying the mathematical basis of the Unruh effect and its relation to a parameter-dependent family of solutions.

Findings

Representation includes a parameter-dependent family of solutions.

Unruh field emerges as a singular limit of the representation.

Mathematical framework clarifies the thermal perception by accelerated detectors.

Abstract

It was suggested by Unruh that a uniformly accelerated detector in vacuum would perceive a noise with a thermal distribution. We obtain a representation of solutions of the wave equation in two dimensions suitable for the Rindler regions. The representation includes the dependence on a parameter. The Unruh field corresponds to a singular limit of the representation.