Elements of Fedosov geometry in Lagrangian BRST Quantization

A Lagrangian formulation of the BRST quantization of generic gauge theories in general irreducible non-Abelian hypergauges is proposed on the basis of the multilevel Batalin–Tyutin formalism and a special BV–BFV dual description of a reducible gauge model on the symplectic supermanifold M0 locally parameterized by the antifields for Lagrangian multipliers and the fields of the BV method. The quantization rules are based on a set of nilpotent anticommuting operators ∆,V,U defined through both odd and even symplectic structures on a supersymplectic manifold M locally representable as an odd (co)tangent bundle over M0 provided by the choice of a flat Fedosov connection and a non-symplectic metric on M0 compatible with it. The generating functional of Green’s functions is constructed in general coordinates on M with the help of contracting homotopy operators with respect to V and U. We prove the gauge independence of the S-matrix and derive the Ward identity.