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Field Theory and infinite dimensional (toroidal) algebra

场论和无限维（环形）代数

基本信息

批准号：
11640275
负责人：
SASAKI Ryu
金额：
$ 2.05万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

项目摘要

We focused on (infinite dimensiona) symmetries, which constitute one of the center pillars of theoretical physics. In particular, we investigated the toroidal algebras appearing in the higher dimensional KWZW(K\"ahler-Wess-Zumino-Witten) models and integrable systems associated with Seiberg-Witten (S-W) theory, namely, elliptic Calogero-Moser(C-M) models. Various forms of symmetry algebras in theoretical physics, in particular, field theory and quantum mechanics are clarified through this research.Main aims of the three year research were :1. realisation of toroidal algebra in infinite dimensional systems (field theories)2. realisation of (degenerate) toroidal algebra in effective field theories (S-W theory, etc) and multi-particle dynamical systems3. clarification of the transition from the toroidal to affine algebras at the levels of Lax-representation and the conserved quantities obtained from it,4. understanding the dynamical meaning of the transition from the toroidal to affine algebras at the levels of classical (and quantum) solutions of elliptic C-M systems and (affine) Toda theories,Sasaki : In the first year, he focused on the C-M models, which are integrable dynamical systems of finite degrees of freedom at the classical and quantum levels. In the second year, quantum C-M systems were investigated. In the third year, the addition of spin degrees of freedom, Hubbard type models, so-called "relativistic generalisation", the quasi-exact integrable extension, i.e. so-called Inozemtsev models, were pursued.Inami : In the first year, the relationship between symmetry algebras appearing in various integrable models and their dynamics was pursued. In the second and third years the same subjects were investigated in more detail and at deeper levels. The ultra violet divergences in three dimensional non-linear sigma models with extended supersymmetry, and kikn solutions, lump solutions of non-linear sigma models were investigated.

我们专注于（无限维）对称性，它构成了理论物理学的中心支柱之一。特别地，我们研究了出现在高维KWZW（Kahler-Wess-Zumino-Witten）模型和与Seiberg-Witten（S-W）理论相关的可积系统，即椭圆Calogero-Moser（C-M）模型中的环面代数.通过本研究，澄清了理论物理，特别是场论和量子力学中各种形式的对称代数。实现环形代数在无限维系统（场论）2。在有效场论（S-W理论等）和多粒子动力学系统中实现（退化）环形代数3。阐明了在Lax-表示水平上从环面代数到仿射代数的过渡以及由此得到的守恒量。理解椭圆C-M系统和（仿射）户田理论的经典（和量子）解水平上从环面到仿射代数过渡的动力学意义，佐佐木：在第一年，他专注于C-M模型，这是经典和量子水平上有限自由度的可积动力学系统。第二年，研究了量子C-M系统。在第三年，除了自旋自由度，哈伯德型模型，所谓的“相对论推广”，准精确可积扩展，即所谓的Inozemtsev模型，进行了追求。稻波：在第一年，对称代数之间的关系出现在各种可积模型和他们的动力学进行了追求。在第二年和第三年，对同样的主题进行了更详细和更深入的调查。研究了具有扩展超对称性的三维非线性sigma模型的紫外发散性，以及非线性sigma模型的Kikn解和集总解。