A deformation quantization theory for noncommutative quantum mechanics
Journal Article
·
· Journal of Mathematical Physics
- Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Av. Campo Grande, 376, 1749-024 Lisboa (Portugal) and Grupo de Fisica Matematica, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal)
- NuHAG Fakultaet fuer Mathematik, Universitaet Wien, Wien 1090 (Austria)
We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].
- OSTI ID:
- 21362167
- Journal Information:
- Journal of Mathematical Physics, Vol. 51, Issue 7; Other Information: DOI: 10.1063/1.3436581; (c) 2010 American Institute of Physics; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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