Algebraic Integration of Sigma Model Field Equations

TL;DR

This paper demonstrates that the dualization algebra of symmetric space coset sigma models forms a Lie algebra, facilitating the local integration of field equations into first-order forms.

Contribution

It establishes the Lie algebra structure of the dualization algebra and shows how it enables the local integration of the sigma model's field equations.

Findings

Proves the dualization algebra is a Lie algebra.

Shows the algebra generates an adjoint representation.

Enables local integration of field equations into first-order form.

Abstract

We prove that the dualization algebra of the symmetric space coset sigma model is a Lie algebra and we show that it generates an appropriate adjoint representation which enables the local integration of the field equations yielding the first-order ones.