A Deformation Quantization Theory for Non-Commutative Quantum Mechanics

We show that the deformation quantization of non-commutative quantum mechanics previously considered by Dias and Prata can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined, and prove a spectral theorem for the star-genvalue equation us...

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Bibliographic Details
Published inarXiv.org
Main Authors Dias, N C, de Gosson, M A, Luef, F, Prata, J N
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.11.2009
Subjects
Deformation
Mathematics - Mathematical Physics
Measurement
Physics - Mathematical Physics
Quantum mechanics
Quantum physics
Quantum theory
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Summary:We show that the deformation quantization of non-commutative quantum mechanics previously considered by Dias and Prata can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined, and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef.
ISSN:2331-8422
DOI:10.48550/arxiv.0911.1209