Wigner Measures in Noncommutative Quantum Mechanics

Details Wigner Measures in Noncommutative Quantum Mechanics Wigner Measures in Noncommutative Quantum Mechanics

2009-07-25

arxiv.org/abs/0907.4438v1

Comm. Math. Phys. 299, 3 (2010) 709

Physics

Mathematical Physics

31 pages, Latex file

Scientific paper

We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner measure, for a Gaussian to be a noncommutative Wigner measure, and derive certain properties of the marginal distributions which are not shared by ordinary Wigner measures. Moreover, we derive the Robertson-Schr\"odinger uncertainty principle. Finally, we show explicitly how the set of noncommutative Wigner measures relates to the sets of Liouville and (commutative) Wigner measures.

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