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

作者：Chowdhury S Hasibul Hassan^*; Ali S Twareque

来源：Journal of Mathematical Physics, 2015, 56(12): 122102.

DOI：10.1063/1.4936312

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(NC), which is the three fold central extension of the Abelian group of R-4. These representations have been exhaustively studied in earlier papers. The group G(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.

• 出版日期2015-12
• 单位南开大学