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Star Product for Second Class Constraint Systems from a BRST Theory | | I.A. Batalin
; M.A. Grigoriev
; S.L. Lyakhovich
; | | Date: |
14 Dec 2000 | | Journal: | Theor.Math.Phys. 128 (2001) 1109-1139; Teor.Mat.Fiz. 128 (2001) 324-360 | | Subject: | High Energy Physics - Theory; Quantum Algebra; Symplectic Geometry; Differential Geometry | hep-th math.DG math.QA math.SG | | 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. | | Source: | arXiv, hep-th/0101089 | | Services: | Forum | Review | PDF | Favorites | |
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