Abstract
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)].
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