On the field analogue of elliptic spin Calogero-Moser model: Lax pair and equations of motion

Autor:	Zotov, A.
Rok vydání:	2024
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	The Lax pair for the field analogue of the classical spin elliptic Calogero-Moser is proposed. Namely, using the previously known Lax matrix we suggest an ansatz for the accompany matrix. The presented construction is valid when the matrix of spin variables ${\mathcal S}\in{\rm Mat}(N,\mathbb C)$ satisfies the condition ${\mathcal S}^2=c_0{\mathcal S}$ with some constant $c_0\in\mathbb C$. It is proved that the Lax pair satisfies the Zakharov-Shabat equation with unwanted term, thus providing equations of motion on the unreduced phase space. The unwanted term vanishes after additional reduction. In the special case ${\rm rank}(\mathcal S)=1$ we show that the reduction provides the Lax pair of the spinless field Calogero-Moser model obtained earlier by Akhmetshin, Krichever and Volvovski. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.13854 Zobrazit plný text záznamu View this record from Arxiv