Journal of Physical Mathematics

On deformed quantum mechanical schemes and *-value equations based on the space-space noncommutative Heisenberg-Weyl group

L. Roman Juarez and Marcos Rosenbaum

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We investigate the Weyl-Wigner-Groenewold-Moyal, the Stratonovich, and the Berezin group quantization schemes for the space-space noncommutative Heisenberg-Weyl group. We show that the *-product for the deformed algebra of Weyl functions for the first scheme is different than that for the other two, even though their respective quantum mechanics' are equivalent as far as expectation values are concerned, provided that some additional criteria are imposed on the implementation of this process. We also show that it is the *-product associated with the Stratonovich and the Berezin formalisms that correctly gives the Weyl symbol of a product of operators in terms of the deformed product of their corresponding Weyl symbols. To conclude, we derive the stronger *-valued equations for the 3 quantization schemes considered and discuss the criteria that are also needed for them to exist.

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J. Phys. Math., Volume 2 (2010), Article ID P100803, 22 pages.

First available in Project Euclid: 22 September 2011

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Primary: 81Q99: None of the above, but in this section 81R60: Noncommutative geometry 81S30: Phase-space methods including Wigner distributions, etc.

Quantum theory Noncommutative geometry Phase-space methods Wigner distributions


Juarez, L. Roman; Rosenbaum, Marcos. On deformed quantum mechanical schemes and *-value equations based on the space-space noncommutative Heisenberg-Weyl group. J. Phys. Math. 2 (2010), Article ID P100803, 22 pages. doi:10.4303/jpm/P100803.

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