International Journal of Theoretical Physics

, Volume 34, Issue 2, pp 189–210 | Cite as

Difference posets and the histories approach to quantum theories

  • Sylvia Pulmannová
Article

Abstract

Direct limits and tensor products of difference posets are studied. In the spirit of a recent paper by Isham, a potential model for an “unsharp histories” approach to quantum theory based on difference posets as abstract models for the set of effects is considered. It is shown that the set of all histories in this approach has an algebraic structure of a difference poset.

Keywords

Field Theory Elementary Particle Quantum Field Theory Tensor Product Potential Model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bennett, M. K., and Foulis, D. (1993).Order,10, 271–282.Google Scholar
  2. Birkhoff, G., and von Neumann, J. (1936).Annals of Mathematics,37, 823–843.Google Scholar
  3. Burmester, P. (1986).A Model Theoretic Oriented Approach to Partial Algebras, Akademie-Verlag, Berlin.Google Scholar
  4. Busch, P., Lahti, P. J., and Mittelstaedt, P. (1991).The Quantum Theory of Measurement, Springer-Verlag, Berlin.Google Scholar
  5. Dvurečenskij, A. (1994). Tensor product of difference posets,Transactions of the American Mathematical Society, to appear.Google Scholar
  6. Dvurečenskij, A., and Pulmannová, S. (1994a).Reports on Mathematical Physics,34, 151–170.Google Scholar
  7. Dvurečenskij, A., and Pulmannová, S. (1994b). Tensor products of D-posets and D-test spaces,Reports on Mathematical Physics,34, to appear.Google Scholar
  8. Foulis, D. J., and Bennett, M. K. (1994). Effect algebras and unsharp quantum logics,Foundations of Physics, to appear.Google Scholar
  9. Foulis, D., and Randall, C. H. (1972).Journal of Mathematical Physics,13, 1667–1675.Google Scholar
  10. Foulis, D. J., Greechie, R., and Rüttimann, G. (1992).International Journal of Theoretical Physics,31, 787–807.Google Scholar
  11. Gell-Mann, M., and Hartle, J. (1990a). Alternative decohering histories in quantum mechanics, inProceedings of the 25th International Conference on High Energy Physics, Singapore, August 2–8, 1990, K. K. Phua and Y. Yamaguchi, eds.), World Scientific, Singapore, pp. 1303–1310.Google Scholar
  12. Gell-Mann, M., and Hartle, J. (1990b). Quantum mechanics in the light of quantum cosmology, inProceedings 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo, 1989, S. Kobayashiet al., eds., Physical Society of Japan, Tokyo, pp. 321–343.Google Scholar
  13. Gell-Mann, M., and Hartle, J. (1990c). Quantum mechanics in the light of quantum cosmology, inComplexity, Entropy and the Physics of Information, SFI Studies in the Science of Complexity, Vol. VIII, W. Zurek, ed.), Addison-Wesley, Reading, Massachusetts, pp. 425–458.Google Scholar
  14. Giuntini, R., and Greuling, H. (1989).Foundations of Physics,19, 931–945.Google Scholar
  15. Guichardet, A. (1972).Symmetric Hilbert Spaces and Related Topics, Springer-Verlag, New York.Google Scholar
  16. Hedlíková, J., and Pulmannová, S. (n.d.). Generalized difference posets, submitted.Google Scholar
  17. Isham, C. J. (n.d.). Quantum logic and the histories approach to quantum theory, Preprint.Google Scholar
  18. Kôpka, F., and Chovanec, F. (1994).Mathematica Slovaca,44, 21–34.Google Scholar
  19. Mittelstaedt, P. (1977).Journal of Philosophical Logic,6, 463–472.Google Scholar
  20. Mittelstaedt, P. (1983). Analysis of the EPR-experiment by relativistic quantum logic, inProceedings International Symposium on Foundations of Quantum Mechanics, Tokyo, pp. 251–255.Google Scholar
  21. Mittelstaedt, P., and Stachow, E. W. (1983).International Journal of Theoretical Physics,22, 517–540.Google Scholar
  22. Navara, M., and Pták, P. (n.d.). Difference posets and orthoalgebras, submitted.Google Scholar
  23. Pulmannová, S. (1994). A remark to orthomodular partial algebras,Demonstratio Mathematica, to appear.Google Scholar
  24. Pulmannová, S. (n.d.). Congruences in partial Abelian semigroups (in preparation).Google Scholar
  25. Pták, P., and Pulmannová, S. (1991).Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht.Google Scholar
  26. Randall, C. H., and Foulis, D. (1973).Journal of Mathematical Physics,14, 1472–1480.Google Scholar
  27. Varadarajan, V. S. (1968/1970).Geometry of Quantum Theory, Vols. 1 and 2, Van Nostrand, Princeton, New Jersey.Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Sylvia Pulmannová
    • 1
  1. 1.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia

Personalised recommendations