Fluctuation-dissipation theorem and the Unruh effect of scalar and Dirac fields

TL;DR

This paper introduces a systematic method using the fluctuation-dissipation theorem to analyze the Unruh effect for scalar and Dirac fields, providing insights into the origin of statistics inversion and confirming the theorem's applicability.

Contribution

It develops a unified approach to calculate Rindler noise for scalar and Dirac fields using fluctuation-dissipation theorems, clarifying the statistics inversion phenomenon.

Findings

Correct calculation of Rindler noise using the method

Insight into the origin of statistics inversion

Validation of fermionic fluctuation-dissipation theorem

Abstract

We present a simple and systematic method to calculate the Rindler noise, which is relevant to the analysis of the Unruh effect, by using the fluctuation-dissipative theorem. To do this, we calculate the dissipative coefficient explicitly from the equations of motion of the detector and the field. This method gives not only the correct answer but also a hint as to the origin of the apparent statistics inversion effect. Moreover, this method is generalized to the Dirac field, by using the fermionic fluctuation-dissipation theorem. We can thus confirm that the fermionic fluctuation-dissipation theorem is working properly.