Skip to main content
Log in

Jauch-Piron property (everywhere!) in the logicoalgebraic foundation of quantum theories

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The Jauch-Piron property of states on a quantum logic is seen to be of considerable importance within the foundation of quantum theories. In this survey we summarize and comment on recent results on the Jauch-Piron property. We also pose a few open problems whose solution may help in further developing quantum theories and noncommutative measure theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Amann, A. (1987). Jauch-Piron States inW *-algebraic quantum mechanics,Journal of Mathematical Physics,28, 2384–2389.

    Google Scholar 

  • Beltrametti, E., and Cassinelli, G. (1981).The Logic of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.

    Google Scholar 

  • Binder, J., and Pták, P. (1990). A representation of orthomodular lattices,Acta Universitatis Carolinae: Mathematica et Physica,31(1), 21–26.

    Google Scholar 

  • Bugajski, S., Busch, P., Cassinelli, G., Lahti, P., and Quadt, P. (n.d.). Sigma-convex structures and classical embeddings of quantum mechanical state spaces, to appear.

  • Bunce, L., and Hamhalter, J. (n.d.). Jauch-Piron states on von Neumann algebras, to appear.

  • Bunce, L., Navara, M., Pták, P., and Wright, J. D. M. (1985). Quantum logics with Jauch-Piron states,Quarterly Journal of Mathematics, Oxford,36, 261–271.

    Google Scholar 

  • De Lucia, P., and Pták, P. (1992). Quantum probability spaces that are nearly classical,Bulletin of the Polish Academy of Sciences: Mathematics,40(2), 163–173.

    Google Scholar 

  • Emch, G. (1972).Algebraic Method in Statistical Mechanics and Quantum Field Theory, Wiley, London, 1972.

    Google Scholar 

  • Gleason, A. M. (1957). Measures on the closed subspaces of a Hilbert space,Journal of Mathematics and Mechanics,6, 885–893.

    Google Scholar 

  • Greechie, R. (1971). Orthomodular lattices admitting no states,Journal of Combinatorial Theory,10A, 119–132.

    Google Scholar 

  • Gudder, S. (1969). Quantum probability spaces,Proceedings of the American Mathematical Society,21, 296–302.

    Google Scholar 

  • Gudder, S. (1979).Stochastic Methods of Quantum Mechanics, North-Holland, Amsterdam.

    Google Scholar 

  • Hamhalter, J. (1993). Pure Jauch-Piron states on von Neumann algebras,Annales de l'Institute Henri Poincaré,58(1), 1–15.

    Google Scholar 

  • Hamhalter, J. (n.d.). The Gleason property and extensions of states, to appear.

  • Itturioz, L. (1986). A representation theory for orthomodular lattices by means of closure spaces,Acta Mathematica Hungarica,47, 145–151.

    Google Scholar 

  • Jauch, J. M. (1968).Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.

    Google Scholar 

  • Kuratowski, K. (1966).Topology II, Academic Press, New York.

    Google Scholar 

  • Majerník, V., and Pulmannová, S. (1992). Bell inequalities on quantum logics,Journal of Mathematical Physics,33(6), 2173–2178.

    Google Scholar 

  • Müller, V. (1993). Jauch-Piron states on concrete quantum logics,International Journal of Theoretical Physics, to appear.

  • Navara, M., and Pták, P. (1989). Almost Boolean orthomodular posets,Journal of Pure and Applied Algebra,60, 105–111.

    Google Scholar 

  • Navara, M., and Rogalewicz, V. (1991). The pasting constructions for orthomodular posets,Mathematische Nachrichten,154, 157–168.

    Google Scholar 

  • Ovchinnikov, P. (1991). On countable models of orthomodular lattices and Jauch-Piron property, inProceedings of the 10th Conference on Probability “Probastat91”, Bratislava, Czechoslovakia.

  • Piron, C. (1976).Foundations of Quantum Physics, Benjamin, Reading, Massachusetts.

    Google Scholar 

  • Pták, P. (1983). Weak dispersion-free states and the hidden variables hypothesis,Journal of Mathematical Physics,24, 839–840.

    Google Scholar 

  • Pták, P. (1985). Extensions of states on logics,Bulletin of the Polish Academy of Sciences: Mathematics,1985, 493–497.

    Google Scholar 

  • Pták, P., and Pulmannová, S. (1991).Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht.

    Google Scholar 

  • Pták, P., and Pulmannová, S. (n.d.). A measure theoretic characterization of Boolean algebras among orthomodular lattices, to appear.

  • Rogalewicz, V. (1991). Jauch-Piron logics with finiteness conditions,International Journal of Theoretical Physics,30, 437–445.

    Google Scholar 

  • Rüttimann, G. (1977). Jauch-Piron states,Journal of Mathematical Physics,18, 189–193.

    Google Scholar 

  • Tkadlec, J. (1991). Partially additive states on orthomodular posets,Colloquium Mathematicum,LXII, 7–14.

    Google Scholar 

  • Tkadlec, J. (1993). Partially additive measures and set representations of orthoposets,Journal of Pure and Applied Algebra, to appear.

  • Zierler, N., and Schlessinger, M. (1965). Boolean embeddings of orthomodular sets of quantum logics,Duke Mathematical Journal,32, 251–262.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pták, P. Jauch-Piron property (everywhere!) in the logicoalgebraic foundation of quantum theories. Int J Theor Phys 32, 1985–1991 (1993). https://doi.org/10.1007/BF00979520

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00979520

Keywords

Navigation