aqora

Irreducible Representations of Fundamental Algebra for Quantum Mechanics on S D and Gauge Structures

Yoshio Ohnuki

Springer eBooksJan 1, 19950 citations

Wigner functions for the Landau problem in noncommutative quantum mechanics

Sayipjamal Dulat A, Kang Li B, Jianhua Wang

Theoretical and Mathematical PhysicsMay 1, 20116 citations

The Wigner Functions for Neutral Particles in an External Electromagnetic Field in Noncommutative Quantum Mechanics

Halqem Nizamidin, Rehimhaji Yakup, Sayipjamal Dulat A +1 more

International Journal of Theoretical PhysicsAug 4, 20140 citations

Wigner Measures in Noncommutative Quantum Mechanics

Catarina Bastos, Nuno Costa Dias, João Nuno Prata

arXiv:0907.4438Communications in Mathematical PhysicsAug 13, 201038 citations

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

S. Hasibul Hassan Chowdhury, S. Twareque Ali

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 GNC, which is the three fold central extension of the Abelian group of ℝ4. These representations have been exhaustively studied in earlier papers. The group GNC 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.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 GNC, which is the three fold central extension of the Abelian group of ℝ4. These representations have been exhaustively studied in earlier papers. The group GNC 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.

arXiv:1506.06341Journal of Mathematical PhysicsDec 1, 201511 citations

Symplectically covariant Schrödinger equation in phase space

Maurice A. de Gosson

A classical theorem of Stone and von Neumann says that the Schrödinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on configuration space. Using the Wigner-Moyal transform we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of square-integrable functions defined on phase space. This allows us to extend the usual Weyl calculus into a phase-space calculus and leads us to a quantum mechanics in phase space, equivalent to standard quantum mechanics. We also briefly discuss the extension of metaplectic operators to phase space and the probabilistic interpretation of the solutions of the phase space Schrödinger equationA classical theorem of Stone and von Neumann says that the Schrödinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on configuration space. Using the Wigner-Moyal transform we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of square-integrable functions defined on phase space. This allows us to extend the usual Weyl calculus into a phase-space calculus and leads us to a quantum mechanics in phase space, equivalent to standard quantum mechanics. We also briefly discuss the extension of metaplectic operators to phase space and the probabilistic interpretation of the solutions of the phase space Schrödinger equation

arXiv:math-ph/0505073Journal of Physics A Mathematical and GeneralOct 5, 200547 citations

Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics

Related papers

Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics

Related papers