(Received June 24, 2002)
We study Moyal quantization for a constrained system. One of the purposes of this work 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 is different from the classical Hamiltonian for a constrained system. This difference is related to the fact that the naively constructed WW correspondence is no longer one-to-one. In the Moyal quantization, the geometrical meaning of the constraints is clear. In the proposal presented here, the second class constraints are incorporated into the definition of the WW correspondence by limiting the phase space to a hypersurface, while we assume canonical commutation relations for the phase space variables. In the case of linear constraints, we confirm that the Moyal brackets between the Weyl symbols yield the same results as those for the constrained system derived using the Dirac bracket formulation.
URL : http://ptp.ipap.jp/link?PTP/108/1123/
DOI : 10.1143/PTP.108.1123