Weyl-Wigner Formulation of Noncommutative Quantum Mechanics

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dc.creatorBastos, Catarina
dc.creatorBertolami, Orfeu
dc.creatorDias, Nuno Costa
dc.creatorPrata, João Nuno
dc.date2006-11-23
dc.date.accessioned2026-07-07T11:59:27Z
dc.date.available2026-07-07T11:59:27Z
dc.descriptionWe address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform and to the Seiberg-Witten map we construct an isomorphism between the operator and the phase space representations of the extended Heisenberg algebra. This map provides a systematic approach to derive the entire structure of noncommutative quantum mechanics in phase space. We construct the extended starproduct, Moyal bracket and propose a general definition of noncommutative states. We study the dynamical and eigenvalue equations of the theory and prove that the entire formalism is independent of the particular choice of Seiberg-Witten map. Our approach unifies and generalizes all the previous proposals for the phase space formulation of noncommutative quantum mechanics. For concreteness we rederive these proposals by restricting our formalism to some 2-dimensional spaces.
dc.descriptionRevtex4, 3 diagrams, 32 pages
dc.identifierhttps://arxiv.org/abs/hep-th/0611257
dc.identifierhttp://arxiv.org/abs/hep-th/0611257
dc.identifierJ.Math.Phys.49:072101,2008
dc.identifierdoi:10.1063/1.2944996
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/206568
dc.subjectHigh Energy Physics - Theory
dc.titleWeyl-Wigner Formulation of Noncommutative Quantum Mechanics
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