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

粒子物理学和凝聚态物理学中许多重要的物理现象及其处理方法都是非微扰性质的，很难求解。同样的问题也出现在低维的物理系统中。它们更容易用严格的方法得到。我们打算发展低维量子场论的物理和数学方法，并追求它们的应用。具体而言，我们计划研究以下问题：1)可解晶格模型/带边界的可积场论的构建及其在凝聚态物理中的应用。2)其他新型可积场论的构建。3)二维量子引力的非微扰方法。4)拓扑重力。5) W_*和W_N代数的表示理论及其在凝聚态物理中的应用。结理论在统计力学中的应用。7) QCD中的非摄动方法和非线性符号。8)超对称和异常在物理中的应用。我们在上面写的大多数问题的研究上都取得了进展。下面我们只列举其中的几个。1)构造了几种可解晶格模型和可积场论[文献8,17]，研究了半线上系统的稳定性问题。韩国团队（南和他的合作者）对这些问题有共同的兴趣，他们交换了意见。作为边界CFT凝聚态物理的一种应用，导出了Kondo问题的有限尺度尺度谱。问题5):W_N代数的表示理论研究取得了进展[11-14]，从W_N代数的表示理论角度研究了Calogero-Sutherland型模型[15,16,19]。南正基也加入了日本队（大竹、松尾）的讨论。问题7)：这个问题主要是由韩国团队（Park和他的合作者）研究的；Inami也加入了讨论。少

项目成果

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）。

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)

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。