Current Algebra of Classical Non-Linear Sigma Models

TL;DR

This paper analyzes the current algebra structure of classical non-linear sigma models on Riemannian manifolds, revealing that including a composite scalar field allows the algebra to close under Poisson brackets.

Contribution

It introduces a new approach by incorporating a composite scalar field to achieve closure of the current algebra in classical non-linear sigma models.

Findings

Inclusion of a composite scalar field enables algebra closure.

The algebra closes under Poisson brackets with the scalar field.

Provides a framework for understanding symmetries in non-linear sigma models.

Abstract

The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current $j_\mu$ associated with the global symmetry of the theory, a composite scalar field $j$, the algebra closes under Poisson brackets.