On the field analogue of elliptic spin Calogero-Moser model: Lax pair and equations of motion
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918097798037504 |
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| author | Zotov, A. |
| author_facet | Zotov, A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the field analogue of elliptic spin Calogero-Moser model: Lax pair and equations of motion Zotov, A. Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics 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. |
| title | On the field analogue of elliptic spin Calogero-Moser model: Lax pair and equations of motion |
| topic | Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2407.13854 |