Eur. Phys. J. Special Topics 226, 2359-2374 (2017)
https://doi.org/10.1140/epjst/e2017-70066-8

Regular Article

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

¹ Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
² Malaysia-Italy Centre of Excellence for Mathematical Sciences, Universiti Putra Malaysia, Serdang, Malaysia

^a e-mail: shhchowdhury@gmail.com
^b e-mail: hisham@upm.edu.my

Received: 1 March 2017
Published online: 19 April 2017

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 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.