BRST Formalism and Zero Locus Reduction

Abstract

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.

21 pages, latex2e, several modifications have been made, main content remains unchanged

References in corpus (2)

• General quantum antibrackets
• Zero Locus Reduction of the BRST Differential

Cited by in corpus (7)

• Local BRST cohomology in gauge theories
• Characteristic classes of gauge systems
• Hamiltonian BRST and Batalin-Vilkovisky formalisms for second quantization of gauge theories
• Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems
• Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket
• Brane current algebras and generalised geometry from QP manifolds
• Higher Courant-Dorfman algebras and associated higher Poisson vertex algebras