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

Hanno Gottschalk
August 25, 2004
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").

Keywords:
Bisognano-Wichmann, Krein spaces, indefinite metric