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

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").

References in corpus (4)

• Analyticity properties and thermal effects for general quantum field theory on de Sitter space-time
• Rationality of conformally invariant local correlation functions on compactified Minkowski space
• Models of local relativistic quantum fields with indefinite metric (in all dimensions)
• Representations of hermitian kernels by means of Krein spaces II. Invariant kernels

Cited by in corpus (1)

• Quantum fields obtained from convoluted generalized white noise never have positive metric