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

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

1997-04-23

arxiv.org/abs/quant-ph/9704039v1

J.Math.Phys. 39 (1998) 6291-6328

Physics

Quantum Physics

46 pages, amstex

Scientific paper

We consider quasi-free stochastically positive ground and thermal states on Weyl algebras in Euclidean time formulation. In particular, we obtain a new derivation of a general form of thermal quasi-free state and give conditions when such state is stochastically positive i.e. when it defines periodic stochastic process with respect to Euclidean time, so called thermal process. Then we show that thermal process completely determines modular structure canonically associated with quasi-free state on Weyl algebra. We discuss a variety of examples connected with free field theories on globally hyperbolic stationary space-times and models of quantum statistical mechanics.

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