An Algebraic Jost-Schroer Theorem for Massive Theories
Abstract
We consider a purely massive local relativistic quantum theory specified by a family of von Neumann algebras indexed by the space-time regions. We assume that, affiliated with the algebras associated to wedge regions, there are operators which create only single particle states from the vacuum (so-called polarization-free generators) and are well-behaved under the space-time translations. Strengthening a result of Borchers, Buchholz and Schroer, we show that then the theory is unitarily equivalent to that of a free field for the corresponding particle type. We admit particles with any spin and localization of the charge in space-like cones, thereby covering the case of string-localized covariant quantum fields.
Cite
@article{arxiv.1012.1454,
title = {An Algebraic Jost-Schroer Theorem for Massive Theories},
author = {Jens Mund},
journal= {arXiv preprint arXiv:1012.1454},
year = {2012}
}
Comments
21 pages. The second (and crucial) hypothesis of the theorem has been relaxed and clarified, thanks to the stimulus of an anonymous referee. (The polarization-free generators associated with wedge regions, which always exist, are assumed to be temperate.)