Two uniqueness results on the Unruh effect and on PCT-symmetry

TL;DR

This paper establishes two new conditions under which the Unruh effect and PCT-symmetry hold, extending their validity to certain field theories not covered by previous proofs, especially those with geometric operator actions.

Contribution

It proves that Borchers' commutation relations imply the Unruh effect and PCT-symmetry when operators act geometrically on local observable nets, broadening the scope of these phenomena.

Findings

Unruh effect and PCT-symmetry are implied by Borchers' relations under geometric action.

Extends validity of these effects to low-dimensional and infinite-component fields.

Provides conditions for these symmetries beyond the finite-component Wightman fields.

Abstract

The Unruh effect and a closely related form of PCT-symmetry have been proved in general for finite-component Wightman fields by Bisognano and Wichmann. While this result incorporates most of the fields occurring in four-dimensional high-energy physics, there still are field theories of interest that are not covered (e.g., low-dimensional anyon fields and infinite-component fields). From the spectrum condition, Borchers has derived a couple of commutation relations which 'almost, but only almost' imply the Unruh effect and PCT-symmetry. We show that this result does imply the Unruh effect and PCT-symmetry provided that the operators involved in Borchers' commutation relations act geometrically on a local net of observables.