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.
Similar content being viewed by others
References
Banai, M. (1981).International Journal of Theoretical Physics,20, 147–169.
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.
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.
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.
Davis, M. (1977).International Journal of Theoretical Physics,16, 867–874.
Dirac, P. A. M. (1928).Proceedings of the Royal Society of London,117, 610.
Dixmier, J., and Douady, A. (1963).Bulletin de la Societe Mathematiques France,91, 227–283.
Feynman, R. P. et al. (1971).Physical Review D 3, 2706.
Finkelstein, D. (1981a). InCurrent Issues in Quantum Logic, E. Beltrametti and B. van Fraassen, eds., Plenum Press, New York.
Finkelstein, D. (1981b). InQuantum Theory and the Structures of Time and Space, Vol. 4, L. Castell et al., eds.. Carl Hanser Verlag, Mundch.
Gleason, A. M. (1957).Journal of Mathematics and Mechanics,6, 885–893.
Heisenberg, W. (1960).The Principles of Quantum Theory. Dover, New York.
Kaiser, G. (1981).Journal of Mathematical Physics,22, 705–714.
Kijowski, J., and Tulszyjew, W. M. (1979).A Symplectic Framework for Field Theories. Springer-Verlag, Berlin.
Kim, Y. S., and Noz, M. E. (1972).Nuovo Cimento,11A, 513; (1974)19A, 657.
Kim, Y. S., et al. (1979).Journal of Mathematical Physics,20, 1341.
Kim, Y. S. et al. (1982)Physical Review D,25, 1740–1743.
Landau, L. D., and Lifshitz, E. M. (1958).Quantum Mechanics, Pergamon, London.
Piron, C. (1976).Foundations of Quantum Physics. Benjamin, Reading Massachusetts.
Prugoveĉki, E. (1978).Physical Review D,18, 3655–3675.
Prugoveĉki, E. (1981).Hadronic Journal,4, 1018–1104.
Prugoveĉki, E. (1982).Foundations of Physics,12, 555–564.
Prugoveĉki, E. (1983).Stochastic Quantum Mechanics and Quantum Space-Time. D. Reidel, Dordrecht.
Sachs, M. (1982).Hadronic Journal,5, 1781–1801.
Santilli, R. M. (1981).Foundations in Physics,11, 383–472.
Snyder, H. S. (1947).Physical Review,71, 38–41.
Takeuti, G. (1978). Two applications of logic to mathematics. Iwanami and Princeton University Press, Tokyo and Princeton.
Takeuti, G. (1981). InCurrent Issues in Quantum Logic, E. Beltrametti and B. van Fraassen, eds. Plenum Press, New York.
Von Neumann, J. (1955).Mathematical Foundation of Quantum Mechanics, Princeton University Press, Princeton.
Wigner, E. P. (1939).Annals of Mathematics,40, 149.
Author information
Authors and Affiliations
Additional information
Supported by the Hungarian Academy of Sciences.
Rights and permissions
About this article
Cite this article
Banai, M. Quantum relativity theory and quantum space-time. Int J Theor Phys 23, 1043–1063 (1984). https://doi.org/10.1007/BF02213416
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02213416