Hidden Symmetries of the Principal Chiral Model and a Nonstandard Loop Algebra

TL;DR

This paper investigates the intricate loop algebra structure of dressing symmetries in the Principal Chiral Model and introduces a novel infinite set of abelian symmetries that preserve the symplectic form on solution space.

Contribution

It reveals the detailed structure of the dressing symmetry loop algebra and uncovers a new class of abelian symmetries preserving the symplectic form.

Findings

Detailed structure of the dressing symmetry loop algebra.

Identification of a new infinite set of abelian symmetries.

Symmetries preserve the symplectic form on solution space.

Abstract

We examine the precise structure of the loop algebra of `dressing' symmetries of the Principal Chiral Model, and discuss a new infinite set of abelian symmetries of the field equations which preserve a symplectic form on the space of solutions.