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The Dirac-Kerr-Newman electron

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Abstract

We discuss the relation between the Kerr-Newman spinning particle and the Dirac electron and show that the Dirac equation may be naturally incorporated into the Kerr-Schild formalism as a master equation controlling the Kerr-Newman geometry. As a result, the Dirac electron acquires an extended space-time structure of the Kerr-Newman geometry: a singular ring of Compton size and a twistorial polarization of the gravitational and electromagnetic fields. The behavior of this Dirac-Kerr-Newman system in weak and slowly changing electromagnetic fields is determined by the wave function of the Dirac equation and is indistinguishable from the behavior of the Dirac electron. The wave function of the Dirac equation plays, in this model, the role of an “order parameter” which controls the dynamics, spin polarization and the twistorial structure of space-time.

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References

  1. R. P. Kerr, Phys. Rev. Lett. 11, 237 (1963).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. E. T. Newman, E. Couch, Chinnapared, A. Exton, A. Prakash, and R. Torrence, J. Math. Phys. 6, 918 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  3. B. Carter, Phys. Rev. 174, 1559 (1968).

    Article  ADS  MATH  Google Scholar 

  4. W. Israel, Phys. Rev. D 2, 641 (1970).

    Article  ADS  MathSciNet  Google Scholar 

  5. G. C. Debney, R. P. Kerr, and A. Schild, J. Math. Phys. 10, 1842 (1969).

    Article  ADS  MathSciNet  Google Scholar 

  6. A. Ya. Burinskii, Sov. Phys. JETP 39, 193 (1974); Russ. Phys. J. 17, 1068 (1974).

    ADS  MathSciNet  Google Scholar 

  7. D. Ivanenko and A. Ya. Burinskii, Russ. Phys. J. 18, 721 (1975).

    Google Scholar 

  8. A. Ya. Burinskii, Strings in the Kerr-Schild Metrics, in “Problems of Theory of Gravitation and Elementary Particles,” (Moscow, Atomizdat 1980), issue 11, p. 47 (in Russian).

    Google Scholar 

  9. D. Ivanenko and A. Ya. Burinskii, Russ. Phys. J. 21, 932 (1978).

    Google Scholar 

  10. C. A. López, Phys. Rev. D 30, 313 (1984).

    Article  ADS  Google Scholar 

  11. R. B. Mann and M. S. Morris, Phys. Lett. A 181, 443 (1993).

    Article  ADS  Google Scholar 

  12. A. Ya. Burinskii, Phys. Lett. A 185, 441 (1994); Stringlike Structures in Complex Kerr Geometry, in Relativity Today, Ed. by R. P. Kerr and Z. Perjés (Akadémiai Kiadó, Budapest, 1994), p. 149.

    Article  ADS  MathSciNet  Google Scholar 

  13. A. Burinskii, Phys. Rev. D 68, 105004 (2003).

    Google Scholar 

  14. A. Burinskii, Phys. Rev. D 70, 086006 (2004).

    Google Scholar 

  15. A. Burinskii, Czech. J. Phys. 55, A261 (2005); hep-th/0412195, hep-th/0412065.

    Article  ADS  Google Scholar 

  16. H. I. Arcos and J. G. Pereira, Gen. Rel. Grav. 36, 2441 (2004).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge Univ. Press, 1982).

  18. B. S. DeWitt, Phys. Rep. C 19, 295 (1975).

    Article  ADS  Google Scholar 

  19. A. Burinskii, Int. J. Geom. Meth. Mod. Phys. 4(3), 437 (2007); Grav. Cosmology 11, 301 (2005); hep-th/0506006.

    Article  MathSciNet  MATH  Google Scholar 

  20. J. Wess and J. Bagger, Supersymmetry and Supergravity (Princeton, New Jersey, 1983).

    MATH  Google Scholar 

  21. A. Burinskii, Phys. Rev. D 67, 124024 (2003); Clas. Quant. Gravity 20, 905 (2003).

    Google Scholar 

  22. R. Penrose, J. Math. Phys. 8, 345 (1967).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. D. Kramer, H. Stephani, E. Herlt, and M. MacCallum, Exact Solutions of Einstein’s Field Equations (Cambridge Univ. Press, 1980).

  24. E. T. Newman, J. Math. Phys. 14, 102 (1973); R. W. Lind and E. T. Newman, J. Math. Phys. 15, 1103 (1974).

    Article  ADS  Google Scholar 

  25. A. Burinskii and R. P. Kerr, Nonstationary Kerr Congruences, gr-qc/9501012.

  26. A. Burinskii and G. Magli, Phys. Rev. D 61, 044017 (2000).

    Google Scholar 

  27. V. B. Berestetsky, E. M. Lifshitz, and L. P. Pitaevsky, Quantum Electrodynamics (Course of Theoretical Physics, 4) (Pergamon, Oxford, UK, 1982).

    Google Scholar 

  28. R. P. Feynman, The Theory of Fundamental Processes (Benjamin, Inc., New York, 1961).

    Google Scholar 

  29. R. P. Kerr and W. B. Willson, Gen. Rel. Grav. 10, 273 (1979).

    Article  ADS  MATH  Google Scholar 

  30. A. Burinskii, Grav. Cosmology 8, 261 (2002).

    ADS  MathSciNet  MATH  Google Scholar 

  31. A. Burinskii, J. Phys. A: Math. Gen. 39, 6209 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. A. Burinskii, E. Elizalde, S. R. Hildebrandt, and G. Magli, Phys. Rev. D 65, 064039 (2002); gr-qc/0109085.

    Google Scholar 

  33. R. Tolman, Relativity, Thermodynamics and Cosmology (Clavendon, Oxford, 1969).

    Google Scholar 

  34. M. Gürses and F. Gürsey, J. Math. Phys. 16, 2385 (1975).

    Article  ADS  Google Scholar 

  35. V. P. Frolov, M. A. Markov, and V. F. Mukhanov, Phys. Lett. B 216, 272 (1989); Phys. Rev. D 41, 383 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  36. A. Burinskii, E. Elisalde, S. Hildebrandt and G. Magli, Aligned Electromagnetic Excitations of a Black Hole and Their Impact on Its Quantum Horizon, ArXiv: 0705.3551 [hep-th].

  37. E. Witten, Comm. Math. Phys. 252, 189 (2004); hep-th/0312171.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. V. P. Nair, Phys. Lett. B 214, 215 (1988).

    Article  ADS  Google Scholar 

  39. A. Burinskii, Grav. Cosmology 10, Nos. 1–2(37–38), 50 (2004); hep-th/0403212.

    ADS  MathSciNet  MATH  Google Scholar 

  40. J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill Book Company, 1964), vol. 1.

  41. A. I. Akhiezer and V. B. Berestetsky, Quantum Electrodynamics (Nauka, Moscow, 1981) (in Russian).

    Google Scholar 

  42. A. Burinskii, Clas. Quant. Gravity 16, 3497 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  43. J. Schwinger, Phys. Rev. 82, 664 (1951).

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

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  1. Gravity Research Group, NSI Russian Academy of Sciences, B. Tulskaya 52, Moscow, 115191, Russia

    A. Burinskii

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Burinskii, A. The Dirac-Kerr-Newman electron. Gravit. Cosmol. 14, 109–122 (2008). https://doi.org/10.1134/S0202289308020011

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