The European Physical Journal Special Topics

, Volume 226, Issue 10, pp 2359–2374 | Cite as

Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics

Regular Article
Part of the following topical collections:
  1. Aspects of Statistical Mechanics and Dynamical Complexity

Abstract

While Wigner functions forming phase space representation of quantum states is a well-known fact, their construction for noncommutative quantum mechanics (NCQM) remains relatively lesser known, in particular with respect to gauge dependencies. This paper deals with the construction of Wigner functions of NCQM for a system of 2-degrees of freedom using 2-parameter families of gauge equivalence classes of unitary irreducible representations (UIRs) of the Lie group GNC which has been identified as the kinematical symmetry group of NCQM in an earlier paper. This general construction of Wigner functions for NCQM, in turn, yields the special cases of Landau and symmetric gauges of NCQM.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S.T. Ali, H. Führ, A.E. Krasowska, Ann. Inst. Henri Poincaré 4, 1015 (2003)CrossRefGoogle Scholar
  2. 2.
    F. Ardalan, H. Arfaei, M.M. Sheikh-Jabbari, JHEP 016, 9902 (1999)Google Scholar
  3. 3.
    S.H.H. Chowdhury, S.T. Ali, J. Phys. A: Math. Theor. 47, 085301 (2014)ADSCrossRefGoogle Scholar
  4. 4.
    S.H.H. Chowdhury, arXiv:1507.01105v3 (2016)
  5. 5.
    S.H.H. Chowdhury, S.T. Ali, J. Math. Phys. 56, 122102 (2016)ADSCrossRefGoogle Scholar
  6. 6.
    S.H.H. Chowdhury, S.T. Ali, J. Math. Phys. 54, 032101 (2013)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    S.-C. Chu, P.-M. Ho, Nucl. Phys. B 550, 151 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    S.-C. Chu, P.-M. Ho, Nucl. Phys. B 568, 447 (2000)ADSCrossRefGoogle Scholar
  9. 9.
    A. Connes, M.R. Douglas, A. Schwarz, JHEP 003, 9802 (1998)Google Scholar
  10. 10.
    T. Curtright, D. Fairlie, C. Zachos, Phys. Rev. D 58, 250027 (1998)CrossRefGoogle Scholar
  11. 11.
    F. Delduc, Q. Duret, F. Gieres, M. Lefrancois, J. Phys.: Conf. Ser. 103, 012020 (2008)Google Scholar
  12. 12.
    S. Doplicher, K. Fredenhagen, J.E. Roberts, Comm. Math. Phys. 172, 187 (1995)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    M.R. Douglas, C.M. Hull, JHEP 008, 9802 (1998)Google Scholar
  14. 14.
    M. Duflo, C.C. Moore, J. Funct. Anal. 21, 209 (1976)CrossRefGoogle Scholar
  15. 15.
    H. Führ, Abstract Harmonic Analysis of Continuous Wavelet Transforms (Springer Lecture Notes in Mathematics, Springer Verlag, Heidelberg, 2005)Google Scholar
  16. 16.
    P.-M. Ho, H.-C. Kao, Phys. Rev. Lett. 88, 151602 (2002)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    R. Kubo, J. Phys. Soc. Jap. 19, 2127 (1964)ADSCrossRefGoogle Scholar
  18. 18.
    H.-W. Lee, Phys. Rep. 259, 147 (1995)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    J.E. Moyal, Math. Proc. Camb. Phil. Soc. 45, 99 (1949)ADSCrossRefGoogle Scholar
  20. 20.
    F. Olivares, F. Pennini, A. Plastino, Physica A 389, 22168 (2010)CrossRefGoogle Scholar
  21. 21.
    V. Schomerus, JHEP 030, 9906 (1999)Google Scholar
  22. 22.
    N. Seiberg, E. Witten, JHEP 032, 9909 (1999)Google Scholar
  23. 23.
    H.S. Snyder, Phys. Rev. 71, 38 (1947)ADSCrossRefGoogle Scholar
  24. 24.
    E. Wigner, Phys. Rev. 40, 749 (1932)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research, Universiti Putra MalaysiaUPM Serdang, SelangorMalaysia
  2. 2.Malaysia-Italy Centre of Excellence for Mathematical Sciences, Universiti Putra MalaysiaSerdangMalaysia

Personalised recommendations