Skip to main content
SpringerLink
Log in

Supersymmetric Content of the Dirac and Duffin-Kemmer-Petiau Equations

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We study subsolutions of the Dirac and Duffin-Kemmer-Petiau equations described in our earlier papers. It is shown that subsolutions of the Duffin-Kemmer-Petiau equations and those of the Dirac equation obey the same Dirac equation with some built-in projection operator. This covariant equation can be referred to as supersymmetric since it has bosonic as well as fermionic degrees of freedom.

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

Access this article

Log in via an institution

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. Jackiw, R., Nair, V.P.: Phys. Rev. D 43, 1933 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  2. Plyushchay, M.S.: Phys. Lett. B 273, 250 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  3. Horváthy, P., Plyushchay, M., Valenzuela, M.: Ann. Phys. 325, 1931 (2010)

    Article  MATH  ADS  Google Scholar 

  4. Horváthy, P., Plyushchay, M., Valenzuela, M.: Phys. Rev. D 81, 127701 (2010)

    Article  ADS  Google Scholar 

  5. Horváthy, P., Plyushchay, M., Valenzuela, M.: J. Math. Phys. 51, 092108 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  6. Horváthy, P., Plyushchay, M., Valenzuela, M.: Phys. Rev. D 77, 025017 (2008)

    Article  ADS  Google Scholar 

  7. Okninski, A.: arXiv:math-ph/0309013 (2003)

  8. Okninski, A.: In: Samoilenko, A. (ed.) Proc. of the Fifth International Conference: Symmetry in Nonlinear Mathematical Physics, Kyiv, 2003, vol. 50, p. 902. Institute of Mathematics of NAS of Ukraine, Kiev (2004), Part 2

    Google Scholar 

  9. Okninski, A.: arXiv:math-ph/0703002 (2007)

  10. Okninski, A.: Acta Phys. Pol. B 12, 87 (1981)

    Google Scholar 

  11. Okninski, A.: Phys. Rev. D 25, 3402 (1982)

    Article  ADS  Google Scholar 

  12. Dirac, P.: Proc. R. Soc. Lond. A 117, 610 (1928)

    Article  ADS  MATH  Google Scholar 

  13. Dirac, P.: Proc. R. Soc. Lond. A 118, 351 (1928)

    Article  ADS  MATH  Google Scholar 

  14. Bjorken, J., Drell, S.: Relativistic Quantum Mechanics. McGraw-Hill, New York (1964)

    Google Scholar 

  15. Berestetskii, V., Lifshits, E., Pitaevskii, L.: Relativistic Quantum Theory. Pergamon, Oxford (1974)

    Google Scholar 

  16. Thaller, B.: The Dirac Equation. Springer, Berlin (1992)

    Google Scholar 

  17. Duffin, R.: Phys. Rev. 54, 1114 (1938)

    Article  MATH  ADS  Google Scholar 

  18. Kemmer, N.: Proc. R. Soc. Lond. A 173, 91 (1939)

    Article  MathSciNet  ADS  Google Scholar 

  19. Kemmer, N.: Proc. Camb. Philos. Soc. 39, 189 (1943)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  20. Petiau, G.: Mem. Acad. Sci. R. Belg. 16(2), 1 (1936). Thesis, Univ. Paris (1936)

    Google Scholar 

  21. Proca, A.: J. Phys. Radium 7, 347 (1936)

    Article  MATH  Google Scholar 

  22. Proca, A.: C.R. Acad. Sci. Paris 1366, 347 (1936)

    Google Scholar 

  23. Lanczos, C.: Z. Phys. 1366, 447 (1929)

    ADS  Google Scholar 

  24. Lanczos, C.: Z. Phys. 1366, 474 (1929)

    ADS  Google Scholar 

  25. Lanczos, C.: Z. Phys. 1366, 484 (1929)

    ADS  Google Scholar 

  26. Bogush, A., Kisel, V., Tokarevskaya, N., Red’kov, V.: Ann. Ann. Fond. Louis Broglie 32, 355 (2007)

    MathSciNet  Google Scholar 

  27. Misner, C., Thorne, K., Wheeler, J.: Gravitation. Freeman, San Francisco (1973)

    Google Scholar 

  28. Corson, E.: Introduction to Tensors, Spinors, and Relativistic Wave-Equations (Relation Structure). Blackie, Glasgow (1953)

    MATH  Google Scholar 

  29. Zralek, M.: Acta Phys. Pol. B 28, 2225 (1997)

    Google Scholar 

  30. Perkins, D.: Introduction to High Energy Physics. The Press Syndicate of the University of Cambridge, Cambridge (2000)

    Google Scholar 

  31. Fukugita, M., Yanagida, T.: Physics of Neutrinos and Applications to Astrophysics. Springer, Berlin (2003)

    Google Scholar 

  32. Majorana, E.: Nuovo Cimento 14, 171 (1937)

    Article  MATH  Google Scholar 

  33. Feynman, R., Gell-Mann, M.: Phys. Rev. 109, 193 (1958)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  34. Wilczek, F.: In: Duplantier, B., Raimond, J.M., Rivasseau, V. (eds.) The Spin. Progress in Mathematical Physics, vol. 55, pp. 61–69. Birkhäuser, Basel (2009)

    Google Scholar 

  35. Leinaas, J.M., Myrheim, J.: Nuovo Cimento 50, 1 (1977)

    Google Scholar 

  36. Wilczek, F.: Phys. Rev. Lett. 48, 1144 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  37. Goldin, G.A., Menikoff, R., Sharp, D.H.: Phys. Rev. Lett. 51, 2246 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  38. Klishevich, S., Plyushchay, M., de Traubenberg, M.: Nucl. Phys. B 616, 419 (2001)

    Article  MATH  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Politechnika Swietokrzyska, Al. 1000-lecia PP 7, 25-314, Kielce, Poland

    Andrzej Okninski

Authors
  1. Andrzej Okninski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrzej Okninski.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Okninski, A. Supersymmetric Content of the Dirac and Duffin-Kemmer-Petiau Equations. Int J Theor Phys 50, 729–736 (2011). https://doi.org/10.1007/s10773-010-0608-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-010-0608-7

Keywords

Search

Navigation