Moyal Quantization for Constrained System

Details Moyal Quantization for Constrained System Moyal Quantization for Constrained System

2002-06-20

arxiv.org/abs/hep-th/0206190v1

Prog.Theor.Phys. 108 (2002) 1123-1141

Physics

High Energy Physics

High Energy Physics - Theory

25 pages

Scientific paper

10.1143/PTP.108.1123

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.

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