{"title":"Gauge equivalence of $$1+1$$ Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model","authors":"K. R. Atalikov, A. V. Zotov","doi":"10.1134/s0040577924060096","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the classical integrable <span>\\((1+1)\\)</span> trigonometric <span>\\(gl_N\\)</span> Landau–Lifshitz models constructed by means of quantum <span>\\(R\\)</span>-matrices that also satisfy the associative Yang–Baxter equation. It is shown that a <span>\\((1+1)\\)</span> 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 <span>\\(R\\)</span>-matrix. The latter generalizes Cherednik’s <span>\\(7\\)</span>-vertex <span>\\(R\\)</span>-matrix in the <span>\\(GL_2\\)</span> case to the case of <span>\\(GL_N\\)</span>. An explicit change of variables between the <span>\\((1+1)\\)</span> models is obtained. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s0040577924060096","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the classical integrable \((1+1)\) trigonometric \(gl_N\) Landau–Lifshitz models constructed by means of quantum \(R\)-matrices that also satisfy the associative Yang–Baxter equation. It is shown that a \((1+1)\) 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 \(R\)-matrix. The latter generalizes Cherednik’s \(7\)-vertex \(R\)-matrix in the \(GL_2\) case to the case of \(GL_N\). An explicit change of variables between the \((1+1)\) models is obtained.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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