Symplectic embedding and Hamilton-Jacobi analysis of Proca model

TL;DR

This paper uses symplectic and Hamilton-Jacobi methods to embed the Abelian Proca model into a gauge-invariant system and analyze its integrability properties, providing new insights into its structure.

Contribution

It introduces a symplectic embedding of the Proca model into a first-class system and explores its integrability via Hamilton-Jacobi formalism, comparing with Dirac scheme.

Findings

Successful embedding of Proca model into gauge-invariant form

Construction of Lie algebra using generalized Poisson brackets

Analysis of integrability properties of the model

Abstract

Following the symplectic approach we show how to embed the Abelian Proca model into a first-class system by extending the configuration space to include an additional pair of scalar fields, and compare it with the improved Dirac scheme. We obtain in this way the desired Wess-Zumino and gauge fixing terms of BRST invariant Lagrangian. Furthermore, the integrability properties of the second-class system described by the Abelian Proca model are investigated using the Hamilton-Jacobi formalism, where we construct the closed Lie algebra by introducing operators associated with the generalized Poisson brackets.