Lagrangian Approach of the First Class Constrained Systems

TL;DR

This paper presents a systematic Lagrangian approach to derive local symmetries in first class constrained systems, specifically applied to abelian Proca and Chern-Simons models, revealing known and novel symmetries.

Contribution

It introduces a method to obtain local symmetries directly in the Lagrangian formalism for constrained systems, avoiding Hamiltonian analysis.

Findings

Recovered the U(1) symmetry for the Proca model.

Discovered new symmetries in the Chern-Simons model.

Provided a systematic derivation method for local symmetries.

Abstract

We show how to systematically derive the exact form of local symmetries for the abelian Proca and CS models, which are converted into first class constrained systems by the BFT formalism, in the Lagrangian formalism. As results, without resorting to a Hamiltonian formulation we obtain the well-known U(1) symmetry for the gauge invariant Proca model, while showing that for the CS model there exist novel symmetries as well as the usual symmetry transformations.