Reduced Sigma-Model on O(N): Hamiltonian Analysis and Poisson Bracket of Lax Connection

TL;DR

This paper analyzes the Hamiltonian structure and integrability of a bosonic sigma-model on O(N), demonstrating classical integrability through Poisson brackets of the Lax connection.

Contribution

It provides a Hamiltonian formalism and computes the Poisson brackets of the Lax connection for the reduced sigma-model on O(N), establishing its classical integrability.

Findings

Poisson bracket of Lax connection components calculated

Structure implies classical integrability of the model

Hamiltonian formalism developed for the sigma-model

Abstract

This short note is devoted to the study of the Hamiltonian formalism and the integrability of the bosonic model introduced in [hep-th/0612079]. We calculate Poisson bracket of spatial components of Lax connection and we argue that its structure implies classical integrability of the theory.