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December 2010 On deformed quantum mechanical schemes and *-value equations based on the space-space noncommutative Heisenberg-Weyl group
L. Roman Juarez, Marcos Rosenbaum
J. Phys. Math. 2: 1-22 (December 2010). DOI: 10.4303/jpm/P100803

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.

Citation

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L. Roman Juarez. Marcos Rosenbaum. "On deformed quantum mechanical schemes and *-value equations based on the space-space noncommutative Heisenberg-Weyl group." J. Phys. Math. 2 1 - 22, December 2010. https://doi.org/10.4303/jpm/P100803

Information

Published: December 2010
First available in Project Euclid: 22 September 2011

zbMATH: 1264.81259
Digital Object Identifier: 10.4303/jpm/P100803

Subjects:
Primary: 81Q99, 81R60, 81S30

Rights: Copyright © 2010 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

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