Stochastically positive structures on Weyl algebras. The case of quasi-free states

Citation
R. Gielerak et al., Stochastically positive structures on Weyl algebras. The case of quasi-free states, J MATH PHYS, 39(12), 1998, pp. 6291-6328
Citations number
53
Categorie Soggetti
Physics
Journal title
JOURNAL OF MATHEMATICAL PHYSICS
ISSN journal
00222488 → ACNP
Volume
39
Issue
12
Year of publication
1998
Pages
6291 - 6328
Database
ISI
SICI code
0022-2488(199812)39:12<6291:SPSOWA>2.0.ZU;2-E
Abstract
We consider quasi-free stochastically positive ground and thermal states on Weyl algebras in the imaginary time formulation. In particular, we obtain a new derivation of a general form of thermal quasi-free state and give con ditions when such a state is stochastically positive, i.e., when it defines a periodic stochastic process with respect to imaginary time, a so-called thermal process. Then we show that the thermal process completely determine s modular structure canonically associated with the quasi-free thermal stat e on Weyl algebra. We discuss a variety of examples connected with free qua ntum field theories on globally hyperbolic stationary space-times and model s of quantum statistical mechanics. (C) 1998 American Institute of Physics. [S0022-2488(98)01712-5].