The Faddeev-Jackiw Approach and the Conformal Affine sl(2) Toda Model Coupled to Matter Field

TL;DR

This paper applies the Faddeev-Jackiw method to analyze the conformal affine sl(2) Toda model coupled to matter, demonstrating its reduction to sine-Gordon or massive Thirring models via Hamiltonian constraints and gauge fixing.

Contribution

It introduces a novel application of the Faddeev-Jackiw approach to this coupled model, elucidating its equivalence to well-known integrable systems.

Findings

Recovery of sine-Gordon model from the Toda model

Recovery of massive Thirring model from the Toda model

Demonstration of Hamiltonian reduction and gauge fixing

Abstract

The conformal affine sl(2) Toda model coupled to matter field is treated as a constrained system in the context of Faddeev-Jackiw and the (constrained) symplectic schemes. We recover from this theory either, the sine-Gordon or the massive Thirring model, through a process of Hamiltonian reduction, considering the equivalence of the Noether and topological currrents as a constraint and gauge fixing the conformal symmetry.