Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-11-23
J.Math.Phys.49:072101,2008
Physics
High Energy Physics
High Energy Physics - Theory
Revtex4, 3 diagrams, 32 pages
Scientific paper
10.1063/1.2944996
We 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.
Bastos Catarina
Bertolami Orfeu
Dias Nuno Costa
Prata Joao Nuno
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