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Title: Wigner functions for noncommutative quantum mechanics: A group representation based construction

This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and those of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.
Authors:
 [1] ;  [2] ;  [3]
  1. Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China)
  2. (Canada)
  3. Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada)
Publication Date:
OSTI Identifier:
22479562
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 12; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMMUTATION RELATIONS; DEGREES OF FREEDOM; FUNCTIONS; IRREDUCIBLE REPRESENTATIONS; POSITION OPERATORS; QUANTUM MECHANICS; SYMMETRY GROUPS