Complex velocity transformations and the Bisognano--Wichmann theorem for quantum fields acting on Krein spaces

TL;DR

This paper extends the Bisognano--Wichmann theorem to quantum fields with indefinite metrics by establishing complex velocity transformations and analyticity properties in Krein spaces.

Contribution

It introduces a method to define complex velocity transformations in indefinite metric quantum field theory, generalizing the BW theorem to Krein space frameworks.

Findings

Existence of a dense set of analytic vectors for velocity transformation generators.

Definition of complex velocity transformations in indefinite metric settings.

Generalization of the Bisognano--Wichmann theorem for Krein space quantum fields.

Abstract

It is proven that in indefinite metric quantum field theory there exists a dense set of analytic vectors for the generator of the one parameter group of x^0-x^1 velocity transformations. This makes it possible to define complex velocity transformations also for the indefinite metric case. In combination with the results of Bros -- Epstein -- Moschella, proving Bisognano--Wichmann (BW) analyticity within the linear program, one then obtains a suitable generalization of the BW theorem for local, relativistic quantum fields acting on Krein spaces ("quantum fields with indefinite metric").