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Functional properties of transition probability spaces. (English) Zbl 0638.03060

It is shown that every (not necessarily symmetric) transition probability space in the sense of B. Mielnik [Commun. Math. Phys. 9, 55-80 (1968; Zbl 0164.295)] can be considered as a functional logic [M. J. Maczyński, Int. J. Theor. Phys. 11, 149-156 (1974)]. A characterization of those functional logics which correspond to transition probability spaces is presented. Meanwhile I found that P. C. Deliyannis [ibid. 23, 217-226 (1984; Zbl 0547.03043)] proved similar results by different methods not using the functional representation of logics.
Reviewer: S.Pulmannová

MSC:

03G12 Quantum logic
81P05 General and philosophical questions in quantum theory
81P20 Stochastic mechanics (including stochastic electrodynamics)
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References:

[1] Mielnik, B., Commun. Math. Phys., 9, 55 (1968)
[2] Ma̧czyński, M., Int. J. Theoret. Phys., 8, 353 (1973)
[3] Ma̧czyński, M., Int. J. Theoret. Phys., 11, 149 (1974)
[4] Belinfante, J., J. Math. Phys., 17, 285 (1976)
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