Construction of Lax Connections by Exponentiation

TL;DR

This paper introduces a novel method to construct Lax connections in two-dimensional integrable sigma models using exponentiation of an operator, simplifying the process by deriving a quadratic relation for flatness.

Contribution

It presents a new exponentiation-based approach for constructing Lax connections, providing a straightforward quadratic relation for ensuring flatness in integrable models.

Findings

Derived a quadratic relation for the operator ensuring flatness.

Established a method for constructing Lax connections via exponentiation.

Simplified the process of identifying flat connections in integrable sigma models.

Abstract

We propose a method for constructing the Lax connection of two-dimensional relativistic integrable sigma models on coset spaces by means of exponentiation of a suitable operator. We derive a simple quadratic relation that this operator must satisfy for an entire one-parameter family of connections to be flat.