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arXiv · 2303.08020

Gauge equivalence between 1+1 rational Calogero-Moser field theory and higher rank Landau-Lifshitz equation

K. Atalikov·A. Zotov
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Abstract

In this paper we study 1+1 field generalization of the rational $N$-body Calogero-Moser model. We show that this model is gauge equivalent to some special higher rank matrix Landau-Lifshitz equation. The latter equation is described in terms of ${\rm GL}_N$ rational $R$-matrix, which turns into the 11-vertex $R$-matrix in the $N=2$ case. The rational $R$-matrix satisfies the associative Yang-Baxter equation, which underlies construction of the Lax pair for the Zakharov-Shabat equation. The field analogue of the IRF-Vertex transformation is proposed. It allows to compute explicit change of variables between the field Calogero-Moser model and the Landau-Lifshitz equation.

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K. Atalikov, A. Zotov. 2023-03-14. Gauge equivalence between 1+1 rational Calogero-Moser field theory and higher rank Landau-Lifshitz equation. https://doi.org/10.1134/s0021364023600714

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