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A martingale characterization of canonical commutation and anticommutation relations. (English) Zbl 0642.60032

Using a martingale condition and some restrictions on moments up to fourth order the characterization problem of boson, fermion, and classical Brownian motions is studied from a unified point of view entirely within the framework of elementary operator theory. Global commutation and anticommutation rules turn out to be consequences of corresponding commutation and anticommutation rules between past and future observables.
Reviewer: Sh.Ayupov

MSC:

60G44 Martingales with continuous parameter
46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras
60J65 Brownian motion
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