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Star Product for Second Class Constraint Systems from a BRST Theory

I. A. Batalin·M. A. Grigoriev·S. L. Lyakhovich
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Abstract

We propose an explicit construction of the deformation quantization of the general second-class constrained system, which is covariant with respect to local coordinates on the phase space. The approach is based on constructing the effective first-class constraint (gauge) system equivalent to the original second-class one and can also be understood as a far-going generalization of the Fedosov quantization. The effective gauge system is quantized by the BFV-BRST procedure. The star product for the Dirac bracket is explicitly constructed as the quantum multiplication of BRST observables. We introduce and explicitly construct a Dirac bracket counterpart of the symplectic connection, called the Dirac connection. We identify a particular star product associated with the Dirac connection for which the constraints are in the center of the respective star-commutator algebra. It is shown that when reduced to the constraint surface, this star product is a Fedosov star product on the constraint surface considered as a symplectic manifold.

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I. A. Batalin, M. A. Grigoriev, S. L. Lyakhovich. 2005-04-16. Star Product for Second Class Constraint Systems from a BRST Theory. https://doi.org/10.1023/a%3A1012387916161

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