Skip to main content
SpringerLink
Log in

Wigner Functions for Klein-Gordon Oscillators in Non-commutative Space

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

Abstract

As a quasi-probability distribution function in phase-space and as well as a special representation of the density matrix, the Wigner function is of great significance in Physics. This letter first makes a review of Wigner function and then provides three approaches of calculating it in non-commutative space. Finally, with the help of Moyal-Weyl multiplication and Bopp’s shift, the Wigner functions for Klein-Gordon oscillators in non-commutative space are deduced explicitly.

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. Wigner, E.: Phys. Rev. 40, 749 (1932)

    Article  MATH  ADS  Google Scholar 

  2. Hai-Woong, L.E.E.: Phys. Rep. 259, 147 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  3. Kurtsiefer, C., Pfau, T., Mlynek, J.: Nature 386, 150 (1997)

    Article  ADS  Google Scholar 

  4. Seiberg, N., Witten, E.: J. High Energy Phys. 032, 9909 (1999). hep-th/9908142

    Google Scholar 

  5. Chaichian, M., Sheikh-Jabbari, M.M., Tureanu, A.: Phys. Rev. Lett. 86, 2716 (2001)

    Article  ADS  Google Scholar 

  6. Chaichian, M., Demichev, A., Presnajder, P., Sheikh-Jabbari, M.M., Tureanu, A.: Nucl. Phys. B 611, 383 (2001). hep-th/0101209

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Chaichian, M., Presnajder, P., Sheikh-Jabbari, M.M., Tureanu, A.: Phys. Lett. B 527 (2002)

  8. Li, K., Wang, J., Chen, C.: Mod. Phys. Lett. A 20, 2165 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Wang, J., Li, K., Liu, P.: High Energy Phys. Nucl. Phys. 30, 378 (2006)

    Google Scholar 

  10. Wang, J., Li, K.: High Energy Phys. Nucl. Phys. 30, 1053 (2006)

    Google Scholar 

  11. Li, K., Chamoun, N.: Chin. Phys. Lett. 23, 1122–1123 (2006)

    Article  ADS  Google Scholar 

  12. Li, K., Cao, X.H., Wang, D.Y.: Chin. Phys. 15(10), 2236 (2006)

    Article  ADS  Google Scholar 

  13. Li, K., Dulat, S.: Eur. Phys. J. C 46, 825 (2006). hep-th/0508193

    Article  MathSciNet  ADS  Google Scholar 

  14. Mirza, B., Zarei, M.: Eur. Phys. J. C 32, 583 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. Li, K., Wang, J.H.: Eur. Phys. J. C 50, 1007 (2007)

    Article  ADS  Google Scholar 

  16. Dulat, S., Li, K.: Eur. Phys. J. C 54, 333 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  17. Wang, J., Li, K.: J. Phys. A 40, 2197 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. Wang, J., Li, K.: Chin. Phys. Lett. 24, 5 (2007)

    Article  ADS  Google Scholar 

  19. Dulat, S., Li, K., Wang, J.: J. Phys. A, Math. Theor. 41, 065303 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  20. Li, K., Dulat, S., Wang, J.: Chin. Phys. B 17(5), 1674 (2008)

    Article  ADS  Google Scholar 

  21. Gamboa, J., Loewe, M., Mendez, F., Rojas, J.C.: Mod. Phys. Lett. A 16, 2075 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  22. Gamboa, J., Loewe, M., Mendez, F., Rojas, J.C.: Phys. Rev. D 64, 067901 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  23. Bellucci, S., Nersessian, A., Sochichiu, C.: Phys. Lett. B 522, 345 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  24. Muthukumar, B., Mitra, P.: Phys. Rev. D 66, 027701 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  25. Dulat, S., Li, K.: High Energy Phys. Nucl. Phys. 33(7), 35 (2008)

    Google Scholar 

  26. Mirza, B., Mohadesi, M.: Commun. Theor. Phys. 42, 664 (2004)

    MATH  MathSciNet  Google Scholar 

  27. Li, J.W.K., Dulat, S.: Chin. Phys. C 33(10), 435 (2008)

    Google Scholar 

  28. Chruscinski, D.: Open Syst. Inf. Dyn. 9, 207–221 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  29. Chruscinski, D.: math-ph/0209008

  30. Jing, S.C., Heng, T.H., Zuo, F.: Phys. Lett. A 335, 185 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  31. Heng, T., Lin, B., Jing, S.: Chin. Phys. Lett. 25, 3535 (2008)

    Article  ADS  Google Scholar 

  32. Wang, J., Li, K., Dulat, S.: Eur. Phys. J. C (2009, submitted). arXiv:0908.1703v1 [hep-th]

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Hangzhou Normal University, Hangzhou, 310036, P.R. China

    Kang Li

  2. Department of Physics, Shaanxi University of Technology, Hanzhong, 723001, P.R. China

    Jianhua Wang & Kai Ma

  3. School of Physics Science and Technology, Xinjiang University, Urumqi, 830046, P.R. China

    Sayipjamal Dulat

Authors
  1. Kang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianhua Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sayipjamal Dulat
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kai Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kang Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, K., Wang, J., Dulat, S. et al. Wigner Functions for Klein-Gordon Oscillators in Non-commutative Space. Int J Theor Phys 49, 134–143 (2010). https://doi.org/10.1007/s10773-009-0186-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-009-0186-8

Search

Navigation