Weyl-Wigner formulation of noncommutative quantum mechanics

• Type: Article in International Scientific Journal
• Date: 2008

Authors

Catarina Bastos (Author) Other; Orfeu Bertolami (Author) Other; Nuno Costa Dias (Author) Other; Joao Nuno Prata (Author) Other

Journal

Title: Journal of Mathematical Physics

Vol. 49

Final page: 072101

ISSN: 0022-2488

Publisher: American Institute of Physics

Indexing

ISI Web of Knowledge - 99 Citations

Scopus - 107 Citations

Scientific classification

FOS: Natural sciences > Physical sciences

Other information

Authenticus ID: P-003-Y6G

DOI: 10.1063/1.2944996

Abstract (EN): We address the phase-space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativities. By resorting to a covariant generalization of the Weyl-Wigner transform and to the Darboux 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 star product and 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 the Darboux 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 two-dimensional spaces. (C) 2008 American Institute of Physics.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 24