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This article is cited in 21 scientific papers (total in 21 papers)
Star Product for Second-Class Constraint Systems from a BRST Theory
I. A. Batalina, M. A. Grigorieva, S. L. Lyakhovichb a P. N. Lebedev Physical Institute, Russian Academy of Sciences
b Tomsk State University
Abstract:
We propose an explicit construction of the deformation quantization of a general second-class constraint system that 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 constraint system and can also be understood as a far-reaching 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.
Received: 03.05.2001
Citation:
I. A. Batalin, M. A. Grigoriev, S. L. Lyakhovich, “Star Product for Second-Class Constraint Systems from a BRST Theory”, TMF, 128:3 (2001), 324–360; Theoret. and Math. Phys., 128:3 (2001), 1109–1139
Linking options:
https://www.mathnet.ru/eng/tmf500https://doi.org/10.4213/tmf500 https://www.mathnet.ru/eng/tmf/v128/i3/p324
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Abstract page: | 424 | Full-text PDF : | 200 | References: | 93 | First page: | 1 |
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