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

Journal Article · Tue Dec 15 04:00:00 EST 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4936312· OSTI ID:22479562

Chowdhury, S. Hasibul Hassan, ^[1]

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1. Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China)

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.

• OSTI ID: 22479562
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 56; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMMUTATION RELATIONS
DEGREES OF FREEDOM
FUNCTIONS
IRREDUCIBLE REPRESENTATIONS
POSITION OPERATORS
QUANTUM MECHANICS
SYMMETRY GROUPS