Gauge equivalence of Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model

We consider the classical integrable trigonometric Landau–Lifshitz models constructed by means of quantum -matrices that also satisfy the associative Yang–Baxter equation. It is shown that a field analogue of the trigonometric Calogero–Moser–Sutherland model is gauge equivalent to the Landau–Lifshit...

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Bibliographic Details
Published in:Theoretical and mathematical physics 2024, Vol.219 (3), p.1004-1017
Main Authors: Atalikov, K. R., Zotov, A. V.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Applications of Mathematics
Equivalence
Field theory
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:We consider the classical integrable trigonometric Landau–Lifshitz models constructed by means of quantum -matrices that also satisfy the associative Yang–Baxter equation. It is shown that a field analogue of the trigonometric Calogero–Moser–Sutherland model is gauge equivalent to the Landau–Lifshitz model that arises from the Antonov–Hasegawa–Zabrodin trigonometric nonstandard -matrix. The latter generalizes Cherednik’s -vertex -matrix in the case to the case of . An explicit change of variables between the models is obtained.
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577924060096