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Conformal Symmetry and Quantum Relativity

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Abstract

The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincare symmetry of field theory can be extended to the larger conformal symmetry. We use these symmetries to define quantum observables associated with positions in space-time, in the spirit of Einstein theory of relativity. This conception of localization may be applied to massive as well as massless fields. Localization observables are defined as to obey Lorentz covariant commutation relations and in particular include a time observable conjugated to energy. While position components do not commute in the presence of a nonvanishing spin, they still satisfy quantum relations which generalize the differential laws of classical relativity. We also give of these observables a representation in terms of canonical spatial positions, canonical spin components, and a proper time operator conjugated to mass. These results plead for a new representation not only of space-time localization but also of motion.

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REFERENCES

  1. A. Einstein, Ann. Phys. 17, 891 (1905).

    Google Scholar 

  2. Special Issue on Time and Frequency, in Proc. IEEE 79, 891–1079 (1991).

  3. H. Salecker and E. P. Wigner, Phys. Rev. 109, 571 (1958).

    Google Scholar 

  4. E. Schrödinger, Berl. Ber. 418 (1930); 63, 144, 238 (1931); Ann. l 'IHP 269 (1931).

  5. M. H. L. Pryce, Proc. Roy. Soc. London A 195, 62 (1948).

    Google Scholar 

  6. T. D. Newton and E. Wigner, Rev. Mod. Phys. 21, 400 (1949).

    Google Scholar 

  7. G. N. Fleming, Phys. Rev. 137, B188 (1965).

    Google Scholar 

  8. A. O. Barut and S. Malin, Rev. Mod. Phys. 40, 632 (1968).

    Google Scholar 

  9. M. Jammer, The Philosophy of Quantum Mechanics (Wiley, New York, 1974), Chap. 5.

    Google Scholar 

  10. C. Rovelli, Phys. Rev. D 42, 2638 (1990); D 43, 442 (1991); Class. Quantum Grav. 8, 297, 317 (1991).

    Google Scholar 

  11. C. J. Isham, in Integrable Systems, Quantum Groups and Quantum Field Theories (Kluwer, 1997), p. 157.

  12. D. N. Page and W. K. Wootters, Phys. Rev. D 27, 2885 (1983).

    Google Scholar 

  13. W. G. Unruh, Int. J. Mod. Phys. 28, 1181 (1989).

    Google Scholar 

  14. C. Rovelli, Nuovo Cimento B 110, 81 (1995).

    Google Scholar 

  15. A. Einstein, Ann. Phys. 18, 639 (1905); ibid., 20, 627 (1906).

    Google Scholar 

  16. H. Bateman, Proc. London Math. Soc. 7, 70 (1908), 8, 223 (1909). E. Cunningham, ibid., 8, 77 (1909).

    Google Scholar 

  17. E. Bessel-Hagen, Math. Ann. 84, 258 (1921).

    Google Scholar 

  18. B. Mashhoon and L. P. Grishchuk, Ap. J. 236, 990 (1980).

    Google Scholar 

  19. W. Pauli, Relativitätstheorie (Encyklopädie der matematischen Wissenschaften, Band V19) (Teubner, 1921). Theory of Relativity (Pergamon, New York, 1958; Dover, New York, 1981).

    Google Scholar 

  20. L. Page, Phys. Rev. 49, 254 (1936); L. Page and N. L. Adams, ibid., 49, 466 (1936). See also H. T. Engstrom and M. Zorn, ibid., 49, 701 (1936) and H. P. Robertson, ibid., 49, 755 (1936).

    Google Scholar 

  21. P. A. M. Dirac, Ann. Math. 37, 429 (1936). See also H. J. Bhabha, Proc. Cambridge Philos. Soc. 32, 622 (1936).

    Google Scholar 

  22. E. L. Hill, Phys. Rev. 67, 358 (1945); 72, 143 (1947).

    Google Scholar 

  23. S. N. Gupta, Science 134, 1360 (1961).

    Google Scholar 

  24. T. Fulton, F. Rohrlich, and L. Witten, Nuovo Cimento 26, 653 (1962); Rev. Mod. Phys. 34, 442 (1962).

    Google Scholar 

  25. B. Binegar, C. Fronsdal, and W. Heidenreich, J. Math. Phys. 24, 2828 (1983).

    Google Scholar 

  26. J. A. Schouten and J. Haantjes, Physica 1, 869 (1934); Koninkl. Ned. Akad. Wet. Proc. 43, 1288 (1940).

    Google Scholar 

  27. A. O. Barut and R. B. Haugen, Ann. Phys. 71, 519 (1972); Nuovo Cimento A 18, 495, 511 (1973).

    Google Scholar 

  28. R. H. Dicke, Phys. Rev. 125, 2163 (1962).

    Google Scholar 

  29. A. D. Sakharov, Sov. Phys. JETP Lett. 20, 81 (1974) [Pisma Zh. Eksp. Teor. Fiz. 20, 189 (1974) ].

    Google Scholar 

  30. F. Hoyle, Ap. J. 196, 661 (1975).

    Google Scholar 

  31. A. O. Barut, Helv. Phys. Acta 46, 496 (1973); A. O. Barut and G. Bornzin, J. Math. Phys. 15, 1000 (1974).

    Google Scholar 

  32. M. T. Jaekel and S. Reynaud, Phys. Rev. Lett. 76, 2407 (1996).

    Google Scholar 

  33. M. T. Jaekel and S. Reynaud, Phys. Lett. A 220, 10 (1996).

    Google Scholar 

  34. M. T. Jaekel and S. Reynaud, EuroPhys. Lett. 38, 1 (1997).

    Google Scholar 

  35. A. Einstein, Jahrb. Radioakt. Elektron. 4, 411 (1907).

    Google Scholar 

  36. C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw Hill, New York, 1985).

    Google Scholar 

  37. M. T. Jaekel and S. Reynaud, Quantum Semiclass. Opt. 7, 499 (1995); Brazilian J. Phys. 25, 315 (1995).

    Google Scholar 

  38. B. de Witt, in Relativity, Groups and Topology, C. de Witt and B. de Witt, eds. (Gordon & Breach, New York, 1963).

    Google Scholar 

  39. J. D. Norton, Rep. Prog. Phys. 56, 791 (1993).

    Google Scholar 

  40. A. O. Barut and R. Raczka, The Theory of Group Representations and Applications (PWN, Warsaw, 1980), Chap. 20.

    Google Scholar 

  41. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).

    Google Scholar 

  42. D. M. Greenberger, J. Math. Phys. 11, 2329, 2341 (1970).

    Google Scholar 

  43. B. Russell, ABC of Relativity ( Allen & Unwin, 1925; reprinted by Routledge, London, 1993).

    Google Scholar 

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Authors
  1. Marc-Thierry Jaekel
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  2. Serge Reynaud
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Jaekel, MT., Reynaud, S. Conformal Symmetry and Quantum Relativity. Foundations of Physics 28, 439–456 (1998). https://doi.org/10.1023/A:1018716111971

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