×

zbMATH — the first resource for mathematics

Compatibility problem in quasi-orthocomplemented posets. (English) Zbl 0776.06006
The author studies several notions of compatibility in quasi- orthocomplemented posets provided some distributivity conditions are fulfilled. As a result, he presents conditions under which Boolean subalgebras can be embedded into a Boolean \(\sigma\)-algebra and builds up the so-called functional calculus for observables.
Reviewer: J.Tkadlec (Praha)

MSC:
06C15 Complemented lattices, orthocomplemented lattices and posets
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] BRABEC J., PTÁK P.: On compatibility in quantum logics. Found. Phys. 12 (1982), 207-212.
[2] DVUREČENSKIJ A., CHOVANEC F.: Fuzzy quantum spaces and compatibility. Internat. J. Theoret. Phys. 9 (1988), 1069-1082. · Zbl 0657.60004
[3] DVUREČENSKIJ A., RIEČAN B.: On joint observables for F-quantum spaces. Busefal 35 (1988), 10-14. · Zbl 0662.03056
[4] GUDDER S. P.: Stochastic Methods in Quantum Mechanics. Elsevier/North-Holand, Amsterdam, 1979. · Zbl 0439.46047
[5] KOLMOGOROV A. N.: Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin, 1933. · Zbl 0007.21601
[6] NEUBRUNN T., PULMANNOVÁ S.: On compatibility in quantum logics. Acta Math. Univ. Comen. 42/43 (1983), 153-168. · Zbl 0539.03045
[7] PTÁK P., PULMANNOVÁ S.: Quantum Logics. (Slovak), Veda, Bratislava, 1989.
[8] RIEČAN B.: A new approach to some notions of statistical quantum mechanics. Busefal 35 (1988), 4-6.
[9] SIKORSKI R.: Boolean Algebras. Springer-Verlag, New York, 1964. · Zbl 0123.01303
[10] VARADARAJAN V. S.: Geometry of Quantum Theory. D. van Nostrand comp., INC, New York, 1968. · Zbl 0155.56802
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.