AIP Digital Archive
In the Becchi–Rouet–Stora–Tyutin (BRST) quantization of gauge theories, the zero locus ZQ of the BRST differential Q carries an (anti)bracket whose parity is opposite to that of the fundamental bracket. Observables of the BRST theory are in a 1:1 correspondence with Casimir functions of the bracket on ZQ. For any constrained dynamical system with the phase space N0 and the constraint surface Σ, we prove its equivalence to the constrained system on the BFV-extended phase space with the constraint surface given by ZQ. Reduction to the zero locus of the differential gives rise to relations between bracket operations and differentials arising in different complexes (the Gerstenhaber, Schouten, Berezin–Kirillov, and Sklyanin brackets); the equation ensuring the existence of a nilpotent vector field on the reduced manifold can be the classical Yang–Baxter equation. We also generalize our constructions to the bi-QP manifolds which from the BRST theory viewpoint correspond to the BRST–anti-BRST-symmetric quantization. © 2001 American Institute of Physics.
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