The complete Faddeev-Jackiw treatment of the $U_{EM}(1)$ gauged SU(2) WZW model

TL;DR

This paper applies the Faddeev-Jackiw method to fully analyze the constrained structure of the two-flavor, four-dimensional gauged SU(2) WZW model coupled to electromagnetism, deriving an unconstrained Coulomb-gauge Lagrangian.

Contribution

It provides a complete, approximation-free Faddeev-Jackiw analysis of the gauged SU(2) WZW model, including explicit constraint solutions and Darboux transformations.

Findings

Derived the unconstrained Coulomb-gauge Lagrangian density.

Explicitly solved the model's constraints.

Demonstrated the Faddeev-Jackiw approach's effectiveness for gauge theories.

Abstract

The two flavour, four dimensional WZW model coupled to electromagnetism, is treated as a constraint system in the context of the Faddeev-Jackiw approach. No approximation is made. Detailed exposition of the calculations is given. Solution of the constraints followed by proper Darboux's transformations leads to an unconstrained Coulomb-gauge Lagrangian density.