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Difference posets and the histories approach to quantum theories

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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.

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References

  1. Bennett, M. K., and Foulis, D. (1993).Order,10, 271–282.

  2. Birkhoff, G., and von Neumann, J. (1936).Annals of Mathematics,37, 823–843.

  3. Burmester, P. (1986).A Model Theoretic Oriented Approach to Partial Algebras, Akademie-Verlag, Berlin.

  4. Busch, P., Lahti, P. J., and Mittelstaedt, P. (1991).The Quantum Theory of Measurement, Springer-Verlag, Berlin.

  5. Dvurečenskij, A. (1994). Tensor product of difference posets,Transactions of the American Mathematical Society, to appear.

  6. Dvurečenskij, A., and Pulmannová, S. (1994a).Reports on Mathematical Physics,34, 151–170.

  7. Dvurečenskij, A., and Pulmannová, S. (1994b). Tensor products of D-posets and D-test spaces,Reports on Mathematical Physics,34, to appear.

  8. Foulis, D. J., and Bennett, M. K. (1994). Effect algebras and unsharp quantum logics,Foundations of Physics, to appear.

  9. Foulis, D., and Randall, C. H. (1972).Journal of Mathematical Physics,13, 1667–1675.

  10. Foulis, D. J., Greechie, R., and Rüttimann, G. (1992).International Journal of Theoretical Physics,31, 787–807.

  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.

  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.

  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.

  14. Giuntini, R., and Greuling, H. (1989).Foundations of Physics,19, 931–945.

  15. Guichardet, A. (1972).Symmetric Hilbert Spaces and Related Topics, Springer-Verlag, New York.

  16. Hedlíková, J., and Pulmannová, S. (n.d.). Generalized difference posets, submitted.

  17. Isham, C. J. (n.d.). Quantum logic and the histories approach to quantum theory, Preprint.

  18. Kôpka, F., and Chovanec, F. (1994).Mathematica Slovaca,44, 21–34.

  19. Mittelstaedt, P. (1977).Journal of Philosophical Logic,6, 463–472.

  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.

  21. Mittelstaedt, P., and Stachow, E. W. (1983).International Journal of Theoretical Physics,22, 517–540.

  22. Navara, M., and Pták, P. (n.d.). Difference posets and orthoalgebras, submitted.

  23. Pulmannová, S. (1994). A remark to orthomodular partial algebras,Demonstratio Mathematica, to appear.

  24. Pulmannová, S. (n.d.). Congruences in partial Abelian semigroups (in preparation).

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

  26. Randall, C. H., and Foulis, D. (1973).Journal of Mathematical Physics,14, 1472–1480.

  27. Varadarajan, V. S. (1968/1970).Geometry of Quantum Theory, Vols. 1 and 2, Van Nostrand, Princeton, New Jersey.

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Pulmannová, S. Difference posets and the histories approach to quantum theories. Int J Theor Phys 34, 189–210 (1995). https://doi.org/10.1007/BF00672802

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Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Tensor Product
  • Potential Model