Field generalization of elliptic Calogero-Moser system in the form of higher rank Landau-Lifshitz model

TL;DR

This paper establishes a gauge equivalence between a field generalization of the elliptic Calogero-Moser system and a higher rank XYZ Landau-Lifshitz model, providing explicit transformations and Poisson structure insights.

Contribution

It introduces an explicit gauge transformation linking the elliptic Calogero-Moser field model to the higher rank XYZ Landau-Lifshitz model, expanding understanding of their integrable structures.

Findings

Proved gauge equivalence between the models.

Derived explicit change of variables and Poisson map.

Enhanced understanding of integrable field models.

Abstract

We prove gauge equivalence between integrable field generalization of the elliptic Calogero-Moser model and the higher rank XYZ Landau-Lifshitz model of vector type on 1+1 dimensional space-time. Explicit formulae for the change of variables are derived, thus providing the Poisson map between these models.