BFV-BRST Quantization of the Proca Model based on the Batalin-Tyutin formalism

TL;DR

This paper applies the Batalin-Tyutin formalism to the Proca model to systematically convert second class constraints into first class, resulting in a BRST-invariant Lagrangian that includes the St"ukelberg scalar.

Contribution

It introduces a systematic Hamiltonian approach to gauge the Proca model, incorporating the St"ukelberg scalar and exploring nonlocal symmetries within the BRST framework.

Findings

Successful conversion of second class to first class constraints

Derivation of a BRST-invariant Lagrangian with St"ukelberg scalar

Discussion of nonlocal symmetry structures in the model

Abstract

We apply the Batalin-Tyutin Hamiltonian method to the Abelian Proca model in order to convert a second class constraint system into a first class one systematically by introducing the new fields. Then, according to the BFV formalism we obtain that the desired resulting Lagrangian preserving standard BRST symmetry naturally includes the well-known St\"ukelberg scalar related to the explicit gauge-breaking effect due to the presence of the mass term. Furthermore, we also discuss the nonlocal symmetry structure of this model in the context of the nonstandard BRST symmetry.