## Journal of Physical Mathematics

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

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 22 September 2011

https://projecteuclid.org/euclid.jpm/1316724048

Digital Object Identifier
doi:10.4303/jpm/P100803

Zentralblatt MATH identifier
1264.81259

#### Citation

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. https://projecteuclid.org/euclid.jpm/1316724048

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