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

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