Moyal Quantization for Constrained System

We study the Moyal quantization for the constrained system. One of the purposes is to give a proper definition of the Wigner-Weyl(WW) correspondence, which connects the Weyl symbols with the corresponding quantum operators. A Hamiltonian in terms of the Weyl symbols becomes different from the classi...

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Bibliographic Details
Published inarXiv.org
Main Authors Hori, Takayuki, Koikawa, Takao, Maki, Takuya
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.06.2002
Subjects
Brackets
Commutation
Constraints
Hyperspaces
Measurement
Symbols
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Summary:We study the Moyal quantization for the constrained system. One of the purposes is to give a proper definition of the Wigner-Weyl(WW) correspondence, which connects the Weyl symbols with the corresponding quantum operators. A Hamiltonian in terms of the Weyl symbols becomes different from the classical Hamiltonian for the constrained system, which is related to the fact that the naively constructed WW correspondence is not one-to-one any more. In the Moyal quantization a geometrical meaning of the constraints is clear. In our proposal, the 2nd class constraints are incorporated into the definition of the WW correspondence by limiting the phasespace to the hypersurface. Even though we assume the canonical commutation relations in the formulation, the Moyal brackets between the Weyl symbols yield the same results as those for the constrained system derived by using the Dirac bracket formulation.
ISSN:2331-8422
DOI:10.48550/arxiv.0206190