A martingale characterization of canonical commutation and anticommutation relations

Accardi, Luigi ; Parthasarathy, K. R. (1988) A martingale characterization of canonical commutation and anticommutation relations Journal of Functional Analysis, 77 (1). pp. 211-231. ISSN 0022-1236

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/002212...

Related URL: http://dx.doi.org/10.1016/0022-1236(88)90085-7

Abstract

Using a martingale condition and some restrictions on moments up to fourth order the characterisation 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.

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