The European Physical Journal Special Topics

, Volume 226, Issue 10, pp 2359–2374

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.

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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

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