Wigner Functions for Noncommutative Quantum Mechanics: a group representation based construction

Abstract

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, {\it viz\/,} using the unitary irreducible representations of the group $\g$, which is the three fold central extension of the abelian group of ${\mathbb{R}}^4$. These representations have been exhaustively studied in earlier papers. The group $\g$ 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.

23 pages, no figure

References in corpus (4)

• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• Magnetic fields in noncommutative quantum mechanics
• On the Plethora of Representations Arising in Noncommutative Quantum Mechanics and An Explicit Construction of Noncommutative 4-tori

Cited by in corpus (9)

• On the Plethora of Representations Arising in Noncommutative Quantum Mechanics and An Explicit Construction of Noncommutative 4-tori
• Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics
• On the optical fields propagation in realistic environments
• On a charged spinless point particle minimally coupled to a constant magnetic field in a noncommutative plane
• Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics
• Quantum simulation of quantum mechanical system with spatial noncommutativity
• Noncommutative coherent states and related aspects of Berezin-Toeplitz quantization
• Deformation of Noncommutative Quantum Mechanics
• Supersymmetric Quantum Mechanics on a noncommutative plane through the lens of deformation quantization