Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics
- 39 Downloads
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 G NC 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.
Unable to display preview. Download preview PDF.
- 2.F. Ardalan, H. Arfaei, M.M. Sheikh-Jabbari, JHEP 016, 9902 (1999)Google Scholar
- 4.S.H.H. Chowdhury, arXiv:1507.01105v3 (2016)
- 9.A. Connes, M.R. Douglas, A. Schwarz, JHEP 003, 9802 (1998)Google Scholar
- 11.F. Delduc, Q. Duret, F. Gieres, M. Lefrancois, J. Phys.: Conf. Ser. 103, 012020 (2008)Google Scholar
- 13.M.R. Douglas, C.M. Hull, JHEP 008, 9802 (1998)Google Scholar
- 15.H. Führ, Abstract Harmonic Analysis of Continuous Wavelet Transforms (Springer Lecture Notes in Mathematics, Springer Verlag, Heidelberg, 2005)Google Scholar
- 21.V. Schomerus, JHEP 030, 9906 (1999)Google Scholar
- 22.N. Seiberg, E. Witten, JHEP 032, 9909 (1999)Google Scholar