Quantum deformation of the Dirac bracket

Abstract

The quantum deformation of the Poisson bracket is the Moyal bracket. We construct quantum deformation of the Dirac bracket for systems which admit global symplectic basis for constraint functions. Equivalently, it can be considered as an extension of the Moyal bracket to second-class constraints systems and to gauge-invariant systems which become second class when gauge-fixing conditions are imposed.

arXiv comment18 pages, REVTeX

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• The Gauged O(3) Sigma Model: Schrödinger Representation and Hamilton-Jacobi Formulation
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