Quantum Field Theories in Low Dimensions and Their Application

低维量子场论及其应用

• 批准号: 06044257
• 负责人: INAMI Takeo
• 金额: --
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Overseas Scientific Survey.
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06044257/
• 关键词: Low dimensional field theory; Integrable field theory; solvafle lattice model; Models with boundaries; 2-dimension al quantum gravity; Walgebras; W代数; アノマリー

Many of the important physical phenomena and the methods to deal with them in particle physics and condensed matter physics are of nonperturbative nature and are difficult to solve. The same type of problems appears in physical systems in low dimensions. They are more easily accessible to rigorous methods.We intended to develop physical and mathematical methods in quantum field theories in low dimensions and to pursue their applications. Specifically we planed to investigate the following problems :1) Construction of solvable lattice models/integrable field theories with boundaries and their application to condensed matter physics.2) Construction of other new types of integrable field theories.3) Non-perturbative methods for 2-dimensional quantum gravity.4) Topological gravity.5) Representation theories of W_* and W_N algebras and their application to condensed matter physics.6) Application of the knot theory to statistical mechanics.7) Nonperturbative methods in QCD and nonlinear sigm … More a model in low dimensions.8) Application of supersymmetry and anomalies to physics.We have made progress in the research of most of the problems written above. We give below only a few of them.Problems 1) We have constructed a few kinds of solvable lattice models and integrable field theories [8,17 of the references] and studied the stability problems in systems on a half line [18]. The Korean team (Nam and his collaborators) has a common interest with lnami and Sasaki on these problems and they have exchnged ideas. As an applicatication of the boundary CFT condensed matter physics, finite-size scaling spectrum in the Kondo problem has been derived [20].Problems 5) : Progress has been made in the representation theoretic studies of W_* algebras [11-14], The Calogero-Sutherland type models has been studied from a representation theoretic viepoint of W_N algebras [15,16,19]. Nam has joined the discussion of the Japanese team (Odake, Matsuo).Problem 7) : This problem has been pursued mainly by the Korean team (Park and his collaborators) ; Inami has joined the discussion [7]. Less

许多重要的物理现象以及在粒子物理和凝结物理物理学中处理它们的方法是非扰动性的，难以解决。相同类型的问题出现在低维度的物理系统中。它们更容易被严格的方法访问。我们旨在在低维度中的量子场理论中开发物理和数学方法并追求其应用。我们计划调查以下问题：1）构建具有边界的可溶解晶格模型/可解决的田野理论及其在凝结物理学上的应用。2）构建其他新型的可集成田间理论的构建。3）二维量子重力的非驱动性方法。4）拓扑的态度。统计力学的结理论。7）QCD和非线性SIGM中的非扰动方法…更多的模型在低维度中。8）在物理学中应用超对称性和异常。我们在上述大多数问题的研究中取得了进展。我们只给出了其中的几个。问题1）我们已经构建了几种可解决的晶格模型和可溶的田间理论[参考文献的8,17]，并研究了半行的系统中的稳定性问题[18]。韩国团队（NAM和他的合作者）与Lnami和Sasaki在这些问题上具有共同的兴趣，并且已经扩展了想法。 As an application of the boundary CFT condensed matter physics, finite-size scaling spectrum in the Kondo problem has been derived [20].Problems 5): Progress has been made in the representation theoretic studies of W_* algebras [11-14], The Calogero-Sutherland type models have been studiod from a representation theoretic viepoint of W_N algebras [15,16,19]. NAM加入了日本团队的讨论（Odake，Matsuo）。 Inami加入了讨论[7]。较少的

项目成果

T.Deguchi: "Multivariable invariants of colored links generalizing the Alexander polynomial" Proc.of the Conf.on Quantum Topology, ed.by D.N.Yetter, World Sci.67-86 (1994)

T.Deguchi：“推广亚历山大多项式的彩色链接的多变量不变量”Proc.of the Conf.on Quantum Topology，由 D.N.Yetter 编辑，World Sci.67-86 (1994)

出口哲生: "Multivariable invariants of colored links generalizing the Alexander polynomial" Proceedings of the Conference on Quantum Topology ed.by D.N.Yetter,World Scientific. 67-86 (1994)

Tetsuo Deguchi：“推广亚历山大多项式的彩色链接的多变量不变量”，D.N.Yetter 编的《量子拓扑会议录》，世界科学杂志 67-86（1994 年）。

H.Awata, M.Fukuma, Y.Matsuo, S.Odake: "Representation Theory of W_<1+*> Algebra" Prog.Theor.Phys.Suppl.Proceedings. 118. 344-373 (1995)

H.Awata、M.Fukuma、Y.Matsuo、S.Odake：“W_<1 *> 代数的表示论”Prog.Theor.Phys.Suppl.Proceedings。

H.Awata, M.Fukuma, Y.Matsuo, S.Odake: "Quasifinite Highest Weight Modules over Super W_<1+*> Algebra" Commun.Math.Phys.(1995)

H.Awata、M.Fukuma、Y.Matsuo、S.Odake：“Super W_<1 *> 代数上的拟有限最高权模块”Commun.Math.Phys.(1995)

S.Fujimoto, N.Kawakami, S.-K.Yang: "Microscopic Calculations of the Finite-Size Scaling Spectrum in the Kondo Problem" Phys.Rev.B50. 1046-1056 (1994)

S.Fujimoto、N.Kawakami、S.-K.Yang：“Kondo 问题中有限尺寸缩放谱的微观计算”Phys.Rev.B50。