Symmetries of SU(2) Skyrmion in Hamiltonian and Lagrangian approaches

TL;DR

This paper investigates the symmetry structure of the SU(2) Skyrmion model using both Hamiltonian and Lagrangian formalisms, applying the BFT and BFV methods to derive BRST invariant gauge-fixed actions.

Contribution

It introduces a comprehensive analysis of the SU(2) Skyrmion's symmetries at both Hamiltonian and Lagrangian levels using BFT and BFV formalisms, including BRST invariance.

Findings

Full symmetry structure characterized at the first class Hamiltonian level.

Derived BRST invariant gauge-fixed Lagrangian from the extended action.

Unified understanding of Skyrmion symmetries in Hamiltonian and Lagrangian frameworks.

Abstract

We apply the Batalin-Fradkin-Tyutin (BFT) method to the SU(2) Skyrmion to study the full symmetry structure of the model at the first class Hamiltonian level. On the other hand, we also analyze the symmetry structure of the action having the WZ term, which corresponds to this Hamiltonian, in the framework of the Lagrangian approach. Furthermore, following the BFV formalism we derive the BRST invariant gauge fixed Lagrangian from the above extended action.