Local Superfield Lagrangian BRST Quantization

TL;DR

This paper develops a superfield Lagrangian BRST quantization framework for non-Abelian hypergauges, extending gauge theories with Grassmann parameters and establishing connections with existing quantization methods.

Contribution

It introduces a $ heta$-local superfield formulation of BRST quantization for reducible gauge theories, including new superfield BRST transformations and gauge independence proofs.

Findings

Constructed superfield generating functionals of Green's functions.

Proved gauge independence of the S-matrix.

Derived Ward identities within the superfield formalism.

Abstract

A $\theta$-local formulation of superfield Lagrangian quantization in non-Abelian hypergauges is proposed on the basis of an extension of general reducible gauge theories to special superfield models with a Grassmann parameter $\theta$. We solve the problem of describing the quantum action and the gauge algebra of an $L$-stage-reducible superfield model in terms of a BRST charge for a formal dynamical system with first-class constraints of $(L+1)$-stage reducibility. Starting from $\theta$-local functions of the quantum and gauge-fixing actions, with an essential use of Darboux coordinates on the antisymplectic manifold, we construct superfield generating functionals of Green's functions, including the effective action. We present two superfield forms of BRST transformations, considered as $\theta$-shifts along vector fields defined by Hamiltonian-like systems constructed in terms of the quantum and gauge-fixing actions and an arbitrary $\theta$-local boson function, as well as in terms of corresponding fermion functionals, through Poisson brackets with opposite Grassmann parities. The gauge independence of the S-matrix is proved. The Ward identities are derived. Connection is established with the BV method, the multilevel Batalin-Tyutin formalism, as well as with the superfield quantization scheme of Lavrov, Moshin, and Reshetnyak, extended to the case of general coordinates.