Quantum logics with classically determined states

Paolo de Lucia; Pavel Pták

Colloquium Mathematicae (1999)

  • Volume: 80, Issue: 1, page 147-154
  • ISSN: 0010-1354

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de Lucia, Paolo, and Pták, Pavel. "Quantum logics with classically determined states." Colloquium Mathematicae 80.1 (1999): 147-154. <http://eudml.org/doc/210700>.

@article{deLucia1999,
author = {de Lucia, Paolo, Pták, Pavel},
journal = {Colloquium Mathematicae},
keywords = {quantum logic (= orthomodular poset); Boolean algebra; state (= probability measure); quantum logic; orthomodular poset; state; probability measure; state-classically-determined logic},
language = {eng},
number = {1},
pages = {147-154},
title = {Quantum logics with classically determined states},
url = {http://eudml.org/doc/210700},
volume = {80},
year = {1999},
}

TY - JOUR
AU - de Lucia, Paolo
AU - Pták, Pavel
TI - Quantum logics with classically determined states
JO - Colloquium Mathematicae
PY - 1999
VL - 80
IS - 1
SP - 147
EP - 154
LA - eng
KW - quantum logic (= orthomodular poset); Boolean algebra; state (= probability measure); quantum logic; orthomodular poset; state; probability measure; state-classically-determined logic
UR - http://eudml.org/doc/210700
ER -

References

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  1. [1] E. Beltranetti and G. Cassinelli, The Logic of Quantum Mechanics, Addison-Wesley, Reading, Mass., 1981. 
  2. [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. Zbl0585.03038
  3. [3] R. Greechie, Orthomodular lattices admitting no states, J. Combin. Theory Ser. A 10 (1971), 119-132. Zbl0219.06007
  4. [4] S. Gudder, Stochastic Methods of Quantum Mechanics, North-Holland, Amsterdam, 1979. Zbl0439.46047
  5. [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. [6] P. de Lucia and P. Pták, Quantum probability spaces that are nearly classical, Bull. Polish Acad. Sci. Math. 40 (1992), 163-173. Zbl0765.60001
  7. [7] V. Müller, Jauch-Piron states on concrete quantum logics, Internat. J. Theoret. Phys. 32 (1993), 433-442. Zbl0791.03039
  8. [8] M. Navara and P. Pták, Almost Boolean orthomodular posets, J. Pure Appl. Algebra 60 (1989), 105-111. Zbl0691.03045
  9. [9] P. Pták, Exotic logics, Colloq. Math. 54 (1987), 1-7. Zbl0639.03063
  10. [10] P. Pták and S. Pulmannová, Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht, 1991. Zbl0743.03039
  11. [11] G. Rüttimann, Jauch-Piron states, J. Math. Phys. 18 (1977), 189-193. Zbl0388.03025
  12. [12] R. Sikorski, Boolean Algebras, Springer, Berlin, 1964. 
  13. [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. [14] J. Tkadlec, Partially additive measures and set representations of orthoposets, J. Pure Appl. Algebra 86 (1993), 79-94. Zbl0777.06009

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