d classical integrable structure of squashed sigma Models-a short summ
d classical integrable structure of squashed sigma Models-a short summ
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d 压缩 sigma 模型的经典可积结构 - 短和
DOI：
10.1088/1742-6596/343/1/012055
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Kentaroh Yoshida
中科院分区：
文献类型：
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作者：
Io Kawaguchi;Kentaroh Yoshida
我们对最近关于在压缩的三维球体上定义的二维非线性西格玛模型的经典可积结构的工作进行了简短的总结。描述经典动力学有两种描述，1）有理描述和2）三角描述。根据描述，可以构造两种不同类型的 Lax 对，并且通过计算满足两种描述中的扩展 Yang-Baxter 方程的经典 r/s 矩阵来显示经典可积性。在前者中，系统被描述为理性类型的可积系统。另一方面，后者被描述为三角型。两个描述之间存在非局部映射并且它们是等价的。这是主要手性模型中左右对偶性的非局部推广。
We give a short summary of our recent works on the classical integrable structure of two-dimensional non-linear sigma models defined on squashed three-dimensional spheres. There are two descriptions to describe the classical dynamics, 1) the rational description and 2) the trigonometric description. It is possible to construct two different types of Lax pairs depending on the descriptions, and the classical integrability is shown by computing classical r/s-matrices satisfying the extended Yang-Baxter equation in both descriptions. In the former the system is described as an integrable system of rational type. On the other hand, in the latter it is described as trigonometric type. There exists a non-local map between the two descriptions and those are equivalent. This is a non-local generalization of the left-right duality in principal chiral models.