Lagrangian approach to local symmetries and self-dual model in gauge invariant formulation

TL;DR

This paper employs a Lagrangian and Hamiltonian framework to embed a mixed-class gauge system into a fully gauge-invariant model, revealing the complete local symmetry structure.

Contribution

It introduces a systematic method to derive full local symmetries of a gauge-invariant Lagrangian from a mixed-class system using the Batalin-Fradkin-Tyutin approach.

Findings

Successfully embedded the self-dual model into a pure first-class system.

Extended gauge invariance was achieved in the resulting Lagrangian.

Provided a concrete example of a Lagrangian approach to local symmetries.

Abstract

Taking the St\"uckelberg Lagrangian associated with the abelian self-dual model of P.K. Townsend et al as a starting point, we embed this mixed first- and second-class system into a pure first-class system by following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin. The resulting Lagrangian possesses an extended gauge invariance and provides a non-trivial example for a general Lagrangian approach to unravelling the full set of local symmetries of a Lagrangian.