Skip to main content
Log in

Singularity-free model of electric charge in physical vacuum: non-zero spatial extent and mass generation

  • Research Article
  • Published:
Central European Journal of Physics

Abstract

We propose a model of a spinless electrical charge as a self-consistent field configuration of the electromagnetic (EM) field interacting with a physical vacuum effectively described by the logarithmic quantum Bose liquid. We show that, in contrast to the EM field propagating in a trivial vacuum, a regular solution does exist, and both its mass and spatial extent emerge naturally from dynamics. It is demonstrated that the charge and energy density distribution acquire Gaussian-like form. The solution in the logarithmic model is stable and energetically favourable, unlike that obtained in a model with a quartic (Higgs-like) potential.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. W. Stern, Science 116, 493 (1952)

    Article  ADS  Google Scholar 

  2. F. J. Dyson, Phys. Rev. 85, 631 (1952)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. L. Van Hove, Physica 18, 145 (1952)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. P. A. M. Dirac, Sci. Am. 208, 45 (1963)

    Article  ADS  Google Scholar 

  5. R. P. Feynman, QED — The Strange Theory of Light and Matter (Penguin, London, 1990)

    Google Scholar 

  6. M. Abraham, Phys. Z. 4, 57 (1902)

    MATH  Google Scholar 

  7. M. Abraham, Ann. Phys.-Berlin 315, 105 (1902)

    Article  ADS  Google Scholar 

  8. H. A. Lorentz, In: Enzyklopädie der Mathematischen Wissenschaften Vol. 5 (Leipzig, Teubner, 1905–1922) 145

    Google Scholar 

  9. R. Gautreau, Phys. Rev. D 31, 1860 (1985)

    Article  ADS  Google Scholar 

  10. W. Appel, M. K. H. Kiessling, Ann. Phys.-New York 289, 24 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. P. A. M. Dirac, P. R. Soc. A 268, 57 (1962)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. P. Gnadig, Z. Kunszt, P. Hasenfratz, J. Kuti, Ann. Phys.-New York 116, 380 (1978)

    Article  ADS  Google Scholar 

  13. T. Fliessbach, Am. J. Phys. 49, 432 (1981)

    Article  ADS  Google Scholar 

  14. A. O. Barut, M. Pavsic, Phys. Lett. B 306, 49 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  15. J. A. Wheeler, Geometrodynamics (Academic Press, New York, 1962)

    MATH  Google Scholar 

  16. M. Born, L. Infeld, P. R. Soc. A 144, 425 (1934)

    Article  ADS  Google Scholar 

  17. K. A. Bronnikov, V. N. Melnikov, G. N. Shikin, K. P. Staniukowicz, Ann. Phys.-New York 118, 84 (1979)

    Article  ADS  Google Scholar 

  18. F. Finster, J. Smoller, S.-T. Yau, Phys. Lett. A 259, 431 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. F. Finster, J. Smoller, S.-T. Yau, Phys. Rev. D 59, 104020 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  20. A. B. Datzeff, Phys. Lett. A 80, 6 (1980)

    Article  ADS  Google Scholar 

  21. W. B. Bonnor, F. I. Cooperstock, Phys. Lett. A 139, 442 (1989)

    Article  ADS  Google Scholar 

  22. L. Herrera, V. Varela, Phys. Lett. A 189, 11 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. M. A. Markov, Ann. Phys.-New York 59, 109 (1970)

    Article  ADS  Google Scholar 

  24. M. A. Markov, V. P. Frolov, Teoreticheskaya i Matematischeskaya Fizika 13, 41 (1972)

    Google Scholar 

  25. E. Ayon-Beato, A. Garcia, Phys. Rev. Lett. 80, 5056 (1998)

    Article  ADS  Google Scholar 

  26. K. A. Bronnikov, Phys. Rev. Lett. 85, 4641 (2000)

    Article  ADS  Google Scholar 

  27. S. Habib Mazharimousavi, M. Halilsoy, Phys. Lett. B 678, 407 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  28. O. B. Zaslavskii, arXiv:1003.2324 [gr-qc]

  29. A. Babin, A. Figotin, arXiv:0812.2686 [physics.classph]

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

    Article  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  33. A. Burinskii, Sov. Phys. JETP-USSR 39, 193 (1974)

    MathSciNet  ADS  Google Scholar 

  34. A. Burinskii, Russ. Phys. J. 17, 1068 (1974)

    Google Scholar 

  35. A. Burinskii, Phys. Rev. D 67, 124024 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  36. A. Burinskii, arXiv:hep-th/0507109

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

    Google Scholar 

  38. C. A. Lopez, Phys. Rev. D 30, 313 (1984)

    Article  ADS  Google Scholar 

  39. C. A. Lopez, Gen. Rel. Grav. 24, 285 (1992)

    Article  ADS  Google Scholar 

  40. M. Israelit, N. Rosen, Gen. Relat. Gravit. 27, 153 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  41. H. I. Arcos, J. G. Pereira, Gen. Relat. Gravit. 36, 2441 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. H. I. Arcos, J. G. Pereira, arXiv:0710.0301 [gr-qc]

  43. A. Burinskii, AIP Conf. Proc. 1424, 26–32 (2012)

    Article  ADS  Google Scholar 

  44. K. A. Bronnikov, G. N. Shikin, In: Classical and Quantum Theory of Gravity, Trudy IF (AN BSSR, Minsk, 1976) 88

    Google Scholar 

  45. J. I. Latorre, P. Pascual, R. Tarrach, Nucl. Phys. B 437, 60 (1995)

    Article  ADS  Google Scholar 

  46. P. A. M. Dirac, Nature 168, 906 (1951)

    Article  MathSciNet  ADS  Google Scholar 

  47. P. A. M. Dirac, Nature 169, 702 (1952)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  48. K. P. Sinha, C. Sivaram, E. C. G. Sudarshan, Found. Phys. 6, 65 (1976)

    Article  ADS  Google Scholar 

  49. K. P. Sinha, C. Sivaram, E. C. G. Sudarshan, Found. Phys. 6, 717 (1976)

    Article  ADS  Google Scholar 

  50. K. P. Sinha, E. C. G. Sudarshan, Found. Phys. 8, 823 (1978)

    Article  ADS  Google Scholar 

  51. G. E. Volovik, International Series of Monographs on Physics 117, 1 (2003)

    MathSciNet  Google Scholar 

  52. K. G. Zloshchastiev, arXiv:0906.4282 [hep-th]

  53. K. G. Zloshchastiev, Phys. Lett. A 375, 2305 (2011)

    Article  ADS  MATH  Google Scholar 

  54. K. G. Zloshchastiev, Acta Phys. Pol. B 42, 261 (2011)

    Article  Google Scholar 

  55. G. Rosen, Phys. Rev. 183, 1186 (1969)

    Article  ADS  Google Scholar 

  56. I. Bialynicki-Birula, J. Mycielski, Ann. Phys.-New York 100, 62 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  57. I. Bialynicki-Birula, J. Mycielski, Commun. Math. Phys. 44, 129 (1975)

    Article  MathSciNet  ADS  Google Scholar 

  58. I. Bialynicki-Birula, J. Mycielski, Phys. Scripta 20, 539 (1979)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  59. A. V. Avdeenkov, K. G. Zloshchastiev, J. Phys. B-At. Mol. Opt. 44, 195303 (2011)

    Article  ADS  Google Scholar 

  60. K. G. Zloshchastiev, Eur. Phys. J. B 85, 273 (2012)

    Article  ADS  Google Scholar 

  61. R. Rajaraman, Solitons and Instantons (North-Holland, Amsterdam, 1982)

    MATH  Google Scholar 

  62. K. G. Zloshchastiev, Phys. Rev. D 61, 125017 (2000)

    Article  ADS  Google Scholar 

  63. K. G. Zloshchastiev, Phys. Lett. B 519, 111 (2001)

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vladimir Dzhunushaliev.

About this article

Cite this article

Dzhunushaliev, V., Zloshchastiev, K.G. Singularity-free model of electric charge in physical vacuum: non-zero spatial extent and mass generation. centr.eur.j.phys. 11, 325–335 (2013). https://doi.org/10.2478/s11534-012-0159-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11534-012-0159-z

Keywords

Navigation