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:
  • 金额:
    $ 2.05万
  • 依托单位:
  • 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学,特别是场论和量子力学中的各种形式的对称代数。三年的研究内容是: 1. 无限维系统中环形代数的实现(场论) 2. 有效场论(S-W 理论等)中环形代数的实现以及多粒子动力系统的过渡阐明。在Lax表示的水平上从环形代数到仿射代数以及从中获得的守恒量,理解从环形过渡的动力学意义。在椭圆 C-M 系统和(仿射)Toda 理论的经典(和量子)解水平上仿射代数,佐佐木:第一年,他专注于 C-M 模型,这是有限自由度的可积动力系统经典和量子水平。第二年,研究了量子 C-M 系统。第三年,我们追求添加自旋自由度、哈伯德型模型、所谓的“相对论广义化”、准精确可积扩展,即所谓的 Inozemtsev 模型。 Inami:在第一年,探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。研究了具有扩展超对称性的三维非线性sigma模型的紫外散度,以及非线性sigma模型的kikn解、块解。

项目成果

期刊论文数量(49)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
R.Caseiro and J.-P.Francoise and R.Sasaki: "Algebraic Linearization of Dynamics of Calogero Type for any Coxeter Group"J.Math.Phys.. 41. 4679-4689 (2000)
R.Caseiro 和 J.-P.Francoise 和 R.Sasaki:“任何 Coxeter 群的 Calogero 型动力学的代数线性化”J.Math.Phys.. 41. 4679-4689 (2000)
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    0
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V.I.Inozemtsev, Ryu Sasaki: "On the integrability of classical Ruijsenaars-Schneider Model of BS_2 type"Mod.Phys.Lett.. A16. 1941-1949 (2001)
V.I.Inozemtsev、Ryu Sasaki:“论 BS_2 型经典 Ruijsenaars-Schneider 模型的可积性”Mod.Phys.Lett.. A16。
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T.Inami,Y.Saito and M.Tamamoto: "On the finiteness of the N=4 Susy nonliear sigma model in three-dimensions"Phys.Lett.B. 495. 245-250 (2000)
T.Inami、Y.Saito 和 M.Tamamoto:“关于三维 N=4 Susy 非线性 sigma 模型的有限性”Phys.Lett.B。
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    0
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A.J.Bordner,Ryu Sasaki and K.Takasaki: "Calogero-Moser Models II : Symmetries and Foldings"Progress of Theoretical Physics. 101. 487-518 (1999)
A.J.Bordner、Ryu Sasaki 和 K.Takasaki:“Calogero-Moser 模型 II:对称性和折叠”理论物理进展。
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    0
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SASAKI Ryu其他文献

SASAKI Ryu的其他文献

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{{ truncateString('SASAKI Ryu', 18)}}的其他基金

Quantum symmetries and solvability
量子对称性和可解性
  • 批准号:
    23540303
  • 财政年份:
    2011
  • 资助金额:
    $ 2.05万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Integrable structure in field theory and string theory
场论和弦论中的可积结构
  • 批准号:
    18340061
  • 财政年份:
    2006
  • 资助金额:
    $ 2.05万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Exactly and quasi-Exactly Solvable multi-particle Quantum Systems and Generalized Supersymmetry
精确和准精确可解的多粒子量子系统和广义超对称性
  • 批准号:
    14540259
  • 财政年份:
    2002
  • 资助金额:
    $ 2.05万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Solvable System with non-trivial Boundary Conditions : Quantum Group and Excahnge Algebra
具有非平凡边界条件的可解系统:量子群和交换代数
  • 批准号:
    06640395
  • 财政年份:
    1994
  • 资助金额:
    $ 2.05万
  • 项目类别:
    Grant-in-Aid for General Scientific Research (C)

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Calogero-Moser correspondence: at the crossroads of representation theory, geometry and integrable systems
卡洛杰罗-莫泽对应:处于表示论、几何和可积系统的十字路口
  • 批准号:
    EP/K004999/1
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  • 财政年份:
    2008
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Exactly and quasi-Exactly Solvable multi-particle Quantum Systems and Generalized Supersymmetry
精确和准精确可解的多粒子量子系统和广义超对称性
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    14540259
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    2002
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    Grant-in-Aid for Scientific Research (C)
Asymptotic Localization, Moser-Calogero Systems and Super Symmetric Yang-Mills Theory
渐近定位、Moser-Calogero 系统和超对称 Yang-Mills 理论
  • 批准号:
    0196550
  • 财政年份:
    2001
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  • 项目类别:
    Standard Grant
Asymptotic Localization, Moser-Calogero Systems and Super Symmetric Yang-Mills Theory
渐近定位、Moser-Calogero 系统和超对称 Yang-Mills 理论
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