International Journal of Theoretical Physics

, Volume 23, Issue 11, pp 1043–1063 | Cite as

Quantum relativity theory and quantum space-time

  • Miklós Banai
Article

Abstract

A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is shown that the quantum space-time models of Banai introduced in another paper is formulated in terms of Davis' quantum relativity. The recently proposed classical relativistic quantum theory of Prugovečki and his corresponding classical relativistic quantum model of space-time open the way to introduce, in a consistent way, the quantum space-time model (the quantum substitute of Minkowski space) of Banai proposed in the paper mentioned. The goal of quantum mechanics of quantum relativistic particles living in this model of space-time is to predict the rest mass system properties of classically relativistic (massive) quantum particles (“elementary particles”). The main new aspect of this quantum mechanics is that provides a true mass eigenvalue problem, and that the excited mass states of quantum relativistic particles can be interpreted as elementary particles. The question of field theory over quantum relativistic model of space-time is also discussed. Finally it is suggested that “quarks” should be considered as quantum relativistic particles.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Banai, M. (1981).International Journal of Theoretical Physics,20, 147–169.Google Scholar
  2. Banai, M. (1982)a. A Space-time quantum hypothesis and the confinement and a model for hadrons, report-KFKI-1982-74.Google Scholar
  3. Banai, M. (1982b).Hadronic Journal,5, 1812–1841; erratum,5, 2155.Google Scholar
  4. Banai, M. (1983)a. Quantum relativity theory, preprint-KFKI-1983-103.Google Scholar
  5. Banai, M. (1983)b. Quantization of space-time and the corresponding quantum mechanics, preprint-KFKI-1983-110.Google Scholar
  6. Banai, M. (1983)c. The canonical quantization of local scalar fields over quantum space-time, preprint-KFKI-1983-51.Google Scholar
  7. Banai, M., and Lukács, B. (1983a).Lettere al Nuovo Cimento,36, 533–538.Google Scholar
  8. Banai, M., and Lukács, B. (1984). On the canonical quantization of local field theories, preprint-KFKI-1984-45.Google Scholar
  9. Brooke, J. A., et al. (1982).Hadronic Journal,5, 1717–1733.Google Scholar
  10. Davis, M. (1977).International Journal of Theoretical Physics,16, 867–874.Google Scholar
  11. Dirac, P. A. M. (1928).Proceedings of the Royal Society of London,117, 610.Google Scholar
  12. Dixmier, J., and Douady, A. (1963).Bulletin de la Societe Mathematiques France,91, 227–283.Google Scholar
  13. Feynman, R. P. et al. (1971).Physical Review D 3, 2706.Google Scholar
  14. Finkelstein, D. (1981a). InCurrent Issues in Quantum Logic, E. Beltrametti and B. van Fraassen, eds., Plenum Press, New York.Google Scholar
  15. Finkelstein, D. (1981b). InQuantum Theory and the Structures of Time and Space, Vol. 4, L. Castell et al., eds.. Carl Hanser Verlag, Mundch.Google Scholar
  16. Gleason, A. M. (1957).Journal of Mathematics and Mechanics,6, 885–893.Google Scholar
  17. Heisenberg, W. (1960).The Principles of Quantum Theory. Dover, New York.Google Scholar
  18. Kaiser, G. (1981).Journal of Mathematical Physics,22, 705–714.Google Scholar
  19. Kijowski, J., and Tulszyjew, W. M. (1979).A Symplectic Framework for Field Theories. Springer-Verlag, Berlin.Google Scholar
  20. Kim, Y. S., and Noz, M. E. (1972).Nuovo Cimento,11A, 513; (1974)19A, 657.Google Scholar
  21. Kim, Y. S., et al. (1979).Journal of Mathematical Physics,20, 1341.Google Scholar
  22. Kim, Y. S. et al. (1982)Physical Review D,25, 1740–1743.Google Scholar
  23. Landau, L. D., and Lifshitz, E. M. (1958).Quantum Mechanics, Pergamon, London.Google Scholar
  24. Piron, C. (1976).Foundations of Quantum Physics. Benjamin, Reading Massachusetts.Google Scholar
  25. Prugoveĉki, E. (1978).Physical Review D,18, 3655–3675.Google Scholar
  26. Prugoveĉki, E. (1981).Hadronic Journal,4, 1018–1104.Google Scholar
  27. Prugoveĉki, E. (1982).Foundations of Physics,12, 555–564.Google Scholar
  28. Prugoveĉki, E. (1983).Stochastic Quantum Mechanics and Quantum Space-Time. D. Reidel, Dordrecht.Google Scholar
  29. Sachs, M. (1982).Hadronic Journal,5, 1781–1801.Google Scholar
  30. Santilli, R. M. (1981).Foundations in Physics,11, 383–472.Google Scholar
  31. Snyder, H. S. (1947).Physical Review,71, 38–41.Google Scholar
  32. Takeuti, G. (1978). Two applications of logic to mathematics. Iwanami and Princeton University Press, Tokyo and Princeton.Google Scholar
  33. Takeuti, G. (1981). InCurrent Issues in Quantum Logic, E. Beltrametti and B. van Fraassen, eds. Plenum Press, New York.Google Scholar
  34. Von Neumann, J. (1955).Mathematical Foundation of Quantum Mechanics, Princeton University Press, Princeton.Google Scholar
  35. Wigner, E. P. (1939).Annals of Mathematics,40, 149.Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • Miklós Banai
    • 1
  1. 1.Central Research Institute for PhysicsBudapest 114Hungary

Personalised recommendations