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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.

我们关注（无限维）对称性，它构成了理论物理学的中心支柱之一。特别是，我们研究了高维KWZW(K\"ahler-Wess-Zumino-Witten)模型中出现的环形代数以及与Seiberg-Witten (S-W)理论相关的可积系统，即椭圆Calogero-Moser(C-M)模型。通过这项研究阐明了理论物理，特别是场论和量子力学中各种形式的对称代数。这三年的研究是：1。无限维系统中环形代数的实现（场论）2。在有效场论（S-W理论等）和多粒子动力系统中实现（简并）环形代数3。澄清在Lax表示的水平上从环形代数到仿射代数的转变以及从中获得的守恒量，4。了解动态在椭圆 C-M 系统和（仿射）Toda 理论的经典（和量子）解水平上从环形代数过渡到仿射代数的意义，佐佐木：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系统。第二年，研究了量子 C-M 系统。第三年，增加了自旋度追求自由、哈伯德型模型、所谓的“相对论概括”、准精确可积扩展，即所谓的 Inozemtsev 模型。 Inami：第一年，研究了各种可积模型中出现的对称代数与其动力学之间的关系。在第二年和第三年，对相同的主题进行了更详细、更深层次的研究。紫外线发散研究了具有扩展超对称性的三维非线性sigma模型，以及非线性sigma模型的kikn解、块解。