Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-01-13
J.Math.Phys. 42 (2001) 3315-3333
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, latex2e, several modifications have been made, main content remains unchanged
Scientific paper
10.1063/1.1367867
In the BRST quantization of gauge theories, the zero locus $Z_Q$ of the BRST differential $Q$ carries an (anti)bracket whose parity is opposite to that of the fundamental bracket. We show that the on-shell BFV/BV gauge symmetries are in a 1:1 correspondence with Hamiltonian vector fields on $Z_Q$, and observables of the BRST theory are in a 1:1 correspondence with characteristic functions of the bracket on $Z_Q$. By reduction to the zero locus, we obtain 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 corresponds to the BRST-anti-BRST-symmetric quantization.
Grigoriev M. A.
Tipunin Yu. I.
~Semikhatov ~M. A.
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