Gauge equivalence of $$1+1$$ Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI:10.1134/s0040577924060096

K. R. Atalikov, A. V. Zotov

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.

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1+1$$卡洛吉罗-莫瑟-萨瑟兰场论与高阶三角兰道-利夫希茨模型的等价性

Abstract 我们考虑了通过量子（R）矩阵构造的经典可积分（(1+1)）三角Landau-Lifshitz模型，这些模型也满足关联Yang-Baxter方程。研究表明，卡洛吉罗-莫泽-萨瑟兰三角非标准$R$-矩阵的$(1+1)$场类似物与Landau-Lifshitz模型是等价的。后者将切雷德尼克在$GL_2$情况下的$7$-顶点$R$-矩阵推广到了$GL_N$情况下。在（(1+1)）模型之间得到了明确的变量变化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

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.