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Communications in Mathematical Physics

, Volume 64, Issue 1, pp 73–82 | Cite as

Relativistic models of nonlinear quantum mechanics

  • T. W. B. Kibble
Article

Abstract

I present and discuss a class of nonlinear quantum-theory models, based on simple relativistic field theories, in which the parameters depend on the state of the system via expectation values of local functions of the fields.

Keywords

Neural Network Statistical Physic Field Theory Complex System Quantum Mechanic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Mielnik, B.: Commun. math. Phys.37, 221 (1974)Google Scholar
  2. 2.
    Bialynicki-Birula, I., Mycielski, J.: Ann Phys.100, 62 (1976)Google Scholar
  3. 3.
    Ludwig, G.: Deutung der Begriffs “physikalische Theorie” und axiomatische Grundlegung der Hilbertraumstruktur der Quantenmechanik durch Hauptsätze der Messens. In: Lecture notes in physics, Vol. 4. Berlin, Heidelberg, New York: Springer 1970Google Scholar
  4. 4.
    Davis, E. B., Lewis, J. T.: Commun. math. Phys.17, 239 (1970)Google Scholar
  5. 5.
    Gunson, J.: Commun. math. Phys.6, 262 (1967)Google Scholar
  6. 6.
    Gudder, S. P.: Four approaches to axiomatic quantum mechanics. In: The uncertainty principle and foundations of quantum mechanics (eds. W. C. Price, S. S. Chissick), p. 247. London: Wiley 1970Google Scholar
  7. 7.
    Edwards, C. M.: Commun. math. Phys.16, 207 (1970)Google Scholar
  8. 8.
    Haag, R., Kastler, D.: J. Math. Phys.5, 848 (1964)Google Scholar
  9. 9.
    Bastin, T. (ed.): Quantum theory and beyond. Cambridge: Cambridge University Press 1971Google Scholar
  10. 10.
    Varadarajan, V. C.: Geometry of quantum mechanics, Vol. I. Princeton, NJ: Van Nostrand 1968Google Scholar
  11. 11.
    Mackey, G. W.: Mathematical foundations of quantum theory. New York: Benjamin 1963Google Scholar
  12. 12.
    Jauch, J. M.: Foundations of quantum mechanics. Reading, Mass.: Addison-Wesley 1968Google Scholar
  13. 13.
    Piron, C.: Foundations of quantum physics. New York, Amsterdam: Benjamin 1976Google Scholar
  14. 14.
    Zabey, P. C.: Found. Phys.5, 323 (1975)Google Scholar
  15. 15.
    Gleason, A. M.: J. Math. Mech.6, 885 (1957)Google Scholar
  16. 16.
    Bell, J. S.: Rev. Mod. Phys.38, 447 (1966)Google Scholar
  17. 17.
    Freedman, S. J., Clauser, J. F.: Phys. Rev. Letters28, 938 (1972)Google Scholar
  18. 18.
    Kasday, L. R., Ullman, J., Wu, C. S.: Bull. Am. Phys. Soc.15, 586 (1971)Google Scholar
  19. 19.
    Faraci, G., Gutkowski, D., Notarrigo, S., Pennisi, A. R.: Lett. Nuovo Cimento9, 607 (1974)Google Scholar
  20. 20.
    Lamehi-Rachti, M., Mittig, W.: Phys. Rev. D14, 2543 (1976)Google Scholar
  21. 21.
    Belinfante, F. J.: A survey of hidden variables theories. Oxford: Pergamon Press 1973Google Scholar
  22. 22.
    de Broglie, L.: Nonlinear wave mechanics. Amsterdam: Elsevier 1960Google Scholar
  23. 23.
    Wigner, E. P.: Remarks on the mind-body question. In: The scientist speculates (ed. I.T. Good). London: Heinemann 1961Google Scholar
  24. 24.
    Schwinger, J.: Phys. Rev.130, 406 (1963)Google Scholar
  25. 25.
    Kibble, T. W. B.: Phys. Rev.150, 1060 (1966)Google Scholar
  26. 26.
    Lee, T. D., Wick, G. C.: Phys. Rev. D9, 2291 (1974)Google Scholar
  27. 27.
    Penrose, R.: Gen. Rel. Grav.7, 171 (1976);7, 31 (1976)Google Scholar
  28. 28.
    Haag, R., Bannier, U.: Commun. math. Phys.60, 1 (1978)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • T. W. B. Kibble
    • 1
  1. 1.Blackett LaboratoryImperial CollegeLondonEngland

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