Quantum logics with classically determined states

• Autorzy: Paolo de Lucia , Pavel Pták
• Języki publikacji: EN

Słowa kluczowe

EN

quantum logic (= orthomodular poset); Boolean algebra; state (= probability measure)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 80
• Numer: 1
• Strony: 147-154

Daty

wydano

1999

otrzymano

1997-05-28

poprawiono

1998-10-26

Twórcy

autor

Paolo de Lucia

• Università degli Studi di Napoli 'Federico II', Dipartimento di Matematica e Applicazioni, Complesso Universitario, Monte S. Angelo, Via Cintia, 80126 Napoli, Italy

autor

Pavel Pták

• Technical University of Prague, Faculty of Electrical Engineering, Department of Mathematics, Technická 2, 166 27 Praha 6, Czech Republic

Bibliografia

• [1] E. Beltranetti and G. Cassinelli, The Logic of Quantum Mechanics, Addison-Wesley, Reading, Mass., 1981.
• [2] L. Bunce, M. Navara, P. Pták and J. D. M. Wright, Quantum logics with Jauch-Piron states, Quart. J. Math. Oxford 36 (1985), 261-271.
• [3] R. Greechie, Orthomodular lattices admitting no states, J. Combin. Theory Ser. A 10 (1971), 119-132.
• [4] S. Gudder, Stochastic Methods of Quantum Mechanics, North-Holland, Amsterdam, 1979.
• [5] P. de Lucia and P. Morales, A non-commutative version of the Alexandroff decomposition theorem in ordered topological groups, Pubblicazioni del Dipartimento di Matematica e Applicazioni 'R. Caccioppoli', Università degli Studi di Napoli 'Federico II', 1993, 1-21.
• [6] P. de Lucia and P. Pták, Quantum probability spaces that are nearly classical, Bull. Polish Acad. Sci. Math. 40 (1992), 163-173.
• [7] V. Müller, Jauch-Piron states on concrete quantum logics, Internat. J. Theoret. Phys. 32 (1993), 433-442.
• [8] M. Navara and P. Pták, Almost Boolean orthomodular posets, J. Pure Appl. Algebra 60 (1989), 105-111.
• [9] P. Pták, Exotic logics, Colloq. Math. 54 (1987), 1-7.
• [10] P. Pták and S. Pulmannová, Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht, 1991.
• [11] G. Rüttimann, Jauch-Piron states, J. Math. Phys. 18 (1977), 189-193.
• [12] R. Sikorski, Boolean Algebras, Springer, Berlin, 1964.
• [13] R. M. Solovay, Real-valued measurable cardinals, in: Axiomatic Set Theory, Proc. Sympos. Pure Math. 13, Part I, Amer. Math. Soc., Providence, R.I., 1971, 397-428.
• [14] J. Tkadlec, Partially additive measures and set representations of orthoposets, J. Pure Appl. Algebra 86 (1993), 79-94.