BRST Quantization of the Proca Model based on the BFT and the BFV Formalism

TL;DR

This paper develops a systematic BRST quantization of the Abelian Proca model using BFT and BFV formalisms, introducing new fields to convert second class constraints into first class, and explores gauge fixing procedures.

Contribution

It presents a simplified approach to convert second class constraints into first class in the Proca model and derives the BRST-invariant Lagrangian including the St"uckelberg scalar.

Findings

The Dirac brackets match the Poisson brackets of extended phase space variables.

The BRST-invariant Lagrangian naturally includes the St"uckelberg scalar.

The approach simplifies the constraint conversion process.

Abstract

The BRST quantization of the Abelian Proca model is performed using the Batalin-Fradkin-Tyutin and the Batalin-Fradkin-Vilkovisky formalism. First, the BFT Hamiltonian method is applied in order to systematically convert a second class constraint system of the model into an effectively first class one by introducing new fields. In finding the involutive Hamiltonian we adopt a new approach which is more simpler than the usual one. We also show that in our model the Dirac brackets of the phase space variables in the original second class constraint system are exactly the same as the Poisson brackets of the corresponding modified fields in the extended phase space due to the linear character of the constraints comparing the Dirac or Faddeev-Jackiw formalisms. Then, according to the BFV formalism we obtain that the desired resulting Lagrangian preserving BRST symmetry in the standard local gauge fixing procedure naturally includes the St\"uckelberg scalar related to the explicit gauge symmetry breaking effect due to the presence of the mass term. We also analyze the nonstandard nonlocal gauge fixing procedure.