Field Generalization of Elliptic Calogero – Moser System in the Form of Higher Rank Landau – Lifshitz Model

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.