Deformation quantization of noncommutative quantum mechanics and dissipation

Details Deformation quantization of noncommutative quantum mechanics and dissipation Deformation quantization of noncommutative quantum mechanics and dissipation

2006-12-21

arxiv.org/abs/hep-th/0612239v1

J.Phys.Conf.Ser.67:012058,2007

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, Latex file, Based on a talk presented by Joao Prata at D.I.C.E. 2006, Piombino, Italy

Scientific paper

10.1088/1742-6596/67/1/012058

We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a $\star$-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner function. The properties of these quasi-distributions are discussed as well as their relation to the sets of ordinary Wigner functions and positive Liouville probability densities. Based on these notions we propose criteria for assessing whether a commutative regime has emerged in the realm of noncommutative quantum mechanics. To induce this noncommutative-commutative transition, we couple a particle to an external bath of oscillators. The master equation for the Brownian particle is deduced.

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