An Embedding of the BV Quantization into an N=1 Local Superfield Formalism

TL;DR

This paper introduces a superfield formulation for Lagrangian quantization in hypergauges, connecting BV and Batalin-Tyutin formalisms, and ensuring gauge independence and deriving Ward identities.

Contribution

It develops a novel N=1 superfield approach to Lagrangian quantization, extending reducible gauge theories with local Grassmann dependence, unifying existing formalisms.

Findings

Constructed superfield generating functionals including the effective action.

Proved gauge-independence of the S-matrix within the superfield formalism.

Established relations between the superfield approach, BV method, and Batalin-Tyutin formalism.

Abstract

We propose an N=1 superfield formulation of Lagrangian quantization in general hypergauges by extending a reducible gauge theory to a superfield model with a local dependence on a Grassmann parameter $\theta$. By means of $\theta$-local functions of the quantum and gauge-fixing actions in terms of Darboux coordinates on the antisymplectic manifold, we construct superfield generating functionals of Green's functions, including the effective action. We prove the gauge-independence of the S-matrix, obtain the Ward identities and establish a relation of the proposed local quantization with the BV method and the multilevel Batalin-Tyutin formalism.