Boundary conditions in the Unruh problem

TL;DR

This paper critically examines the Unruh effect within quantum field theory, demonstrating that boundary conditions and causal separation in Rindler wedges prevent thermalization, challenging the traditional understanding of the effect.

Contribution

The authors show that the Unruh quantization scheme is valid only in the double Rindler wedge and argue that boundary conditions prevent the Unruh effect from arising.

Findings

Unruh quantization is valid only in the double Rindler wedge.

Boundary conditions act as topological obstacles preventing correlations.

Elimination of 'left' degrees of freedom does not affect Rindler observers.

Abstract

We have analyzed the Unruh problem in the frame of quantum field theory and have shown that the Unruh quantization scheme is valid in the double Rindler wedge rather than in Minkowski spacetime. The double Rindler wedge is composed of two disjoint regions ($R$- and $L$-wedges of Minkowski spacetime) which are causally separated from each other. Moreover the Unruh construction implies existence of boundary condition at the common edge of $R$- and $L$-wedges in Minkowski spacetime. Such boundary condition may be interpreted as a topological obstacle which gives rise to a superselection rule prohibiting any correlations between $r$- and $l$- Unruh particles. Thus the part of the field from the $L$-wedge in no way can influence a Rindler observer living in the $R$-wedge and therefore elimination of the invisible "left" degrees of freedom will take no effect for him. Hence averaging over states of the field in one wedge can not lead to thermalization of the state in the other. This result is proved both in the standard and algebraic formulations of quantum field theory and we conclude that principles of quantum field theory does not give any grounds for existence of the "Unruh effect".