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Quantum relativity theory and quantum space-time

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.

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References

  • Banai, M. (1981).International Journal of Theoretical Physics,20, 147–169.

    Google Scholar 

  • Banai, M. (1982)a. A Space-time quantum hypothesis and the confinement and a model for hadrons, report-KFKI-1982-74.

  • Banai, M. (1982b).Hadronic Journal,5, 1812–1841; erratum,5, 2155.

    Google Scholar 

  • Banai, M. (1983)a. Quantum relativity theory, preprint-KFKI-1983-103.

  • Banai, M. (1983)b. Quantization of space-time and the corresponding quantum mechanics, preprint-KFKI-1983-110.

  • Banai, M. (1983)c. The canonical quantization of local scalar fields over quantum space-time, preprint-KFKI-1983-51.

  • Banai, M., and Lukács, B. (1983a).Lettere al Nuovo Cimento,36, 533–538.

    Google Scholar 

  • Banai, M., and Lukács, B. (1984). On the canonical quantization of local field theories, preprint-KFKI-1984-45.

  • Brooke, J. A., et al. (1982).Hadronic Journal,5, 1717–1733.

    Google Scholar 

  • Davis, M. (1977).International Journal of Theoretical Physics,16, 867–874.

    Google Scholar 

  • Dirac, P. A. M. (1928).Proceedings of the Royal Society of London,117, 610.

    Google Scholar 

  • Dixmier, J., and Douady, A. (1963).Bulletin de la Societe Mathematiques France,91, 227–283.

    Google Scholar 

  • Feynman, R. P. et al. (1971).Physical Review D 3, 2706.

    Google Scholar 

  • Finkelstein, D. (1981a). InCurrent Issues in Quantum Logic, E. Beltrametti and B. van Fraassen, eds., Plenum Press, New York.

    Google Scholar 

  • 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 

  • Gleason, A. M. (1957).Journal of Mathematics and Mechanics,6, 885–893.

    Google Scholar 

  • Heisenberg, W. (1960).The Principles of Quantum Theory. Dover, New York.

    Google Scholar 

  • Kaiser, G. (1981).Journal of Mathematical Physics,22, 705–714.

    Google Scholar 

  • Kijowski, J., and Tulszyjew, W. M. (1979).A Symplectic Framework for Field Theories. Springer-Verlag, Berlin.

    Google Scholar 

  • Kim, Y. S., and Noz, M. E. (1972).Nuovo Cimento,11A, 513; (1974)19A, 657.

    Google Scholar 

  • Kim, Y. S., et al. (1979).Journal of Mathematical Physics,20, 1341.

    Google Scholar 

  • Kim, Y. S. et al. (1982)Physical Review D,25, 1740–1743.

    Google Scholar 

  • Landau, L. D., and Lifshitz, E. M. (1958).Quantum Mechanics, Pergamon, London.

    Google Scholar 

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

    Google Scholar 

  • Prugoveĉki, E. (1978).Physical Review D,18, 3655–3675.

    Google Scholar 

  • Prugoveĉki, E. (1981).Hadronic Journal,4, 1018–1104.

    Google Scholar 

  • Prugoveĉki, E. (1982).Foundations of Physics,12, 555–564.

    Google Scholar 

  • Prugoveĉki, E. (1983).Stochastic Quantum Mechanics and Quantum Space-Time. D. Reidel, Dordrecht.

    Google Scholar 

  • Sachs, M. (1982).Hadronic Journal,5, 1781–1801.

    Google Scholar 

  • Santilli, R. M. (1981).Foundations in Physics,11, 383–472.

    Google Scholar 

  • Snyder, H. S. (1947).Physical Review,71, 38–41.

    Google Scholar 

  • Takeuti, G. (1978). Two applications of logic to mathematics. Iwanami and Princeton University Press, Tokyo and Princeton.

    Google Scholar 

  • Takeuti, G. (1981). InCurrent Issues in Quantum Logic, E. Beltrametti and B. van Fraassen, eds. Plenum Press, New York.

    Google Scholar 

  • Von Neumann, J. (1955).Mathematical Foundation of Quantum Mechanics, Princeton University Press, Princeton.

    Google Scholar 

  • Wigner, E. P. (1939).Annals of Mathematics,40, 149.

    Google Scholar 

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Supported by the Hungarian Academy of Sciences.

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Banai, M. Quantum relativity theory and quantum space-time. Int J Theor Phys 23, 1043–1063 (1984). https://doi.org/10.1007/BF02213416

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  • DOI: https://doi.org/10.1007/BF02213416

Keywords

  • Quantum Mechanic
  • Arena
  • Minkowski Space
  • True Mass
  • System Property