Conformal Field Theory Vol.1(共形场论)(第1卷)(经典名著系列)
分類: 图书,科学与自然,物理学,物理学理论,
品牌: 菲利普迪弗朗切斯科
基本信息·出版社:世界图书出版公司
·页码:454 页
·出版日期:2009年
·ISBN:7506292610
·条形码:9787506292610
·包装版本:1版
·装帧:平装
·开本:24
·正文语种:英语
·丛书名:经典名著系列
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内容简介《onformal Field Theory Vol.1(共形场论)》共18章,分为3个部分。
第1部分——简介。第1章中对《onformal Field Theory Vol.1(共形场论)》涉及的相关概念进行了简单回顾。第2章是量子场论的一些基本概念,如自由玻色(费米)子,路径积分,关联函数,对称与守恒量,以及能动张量。第3章则涉及统计力学的一些基本概念,如玻尔兹曼分布,临界现象,重整化群和转移矩阵。
第2部分——基础理论。首先,第4章介绍了全局的共形不变。然后,第5章详细论述了有关二维共形不变基本而重要的概念,内容包括初级场、关联函数、Ward恒等式、自由场、算子积展开和中心荷等等。第6章则是更为详细论述算子表述下的共形场论,此章的重点是Vimsoro代数:和顶点代数。随后两章论述了极小模型,极小模型是共形场论中最重要的模型之一。第9章和第10章分别介绍库仑气体和模不变,屏蔽算子和Verlinde公式等重要概念亦先后引入。第11、12两章分别介绍了Q-态Potts模型和二维Ising模型。
第3部分——具有李群对称性的共形场论。第13章介绍了单李代数的一些基本内容,如单李代数的结构,最高权表示和特征标等等。第14章为仿射李代数(亦称Kac-Moody代数),内容基本与第13章平行。第15~17章,讨论的主题都是WZW(Wess-Zumino.Witten)模型。WZW模型是二维共形场论中另一个最重要的模型,它集中体现了二维共形场论的各种性质。最后一章,即18章为陪集构造。陪集构造是共形场论最重要的手段之一。对于物理学或是数学工作者而言,陪集构造方法将二维共形场论的研究带入到一个新的天地。
《onformal Field Theory Vol.1(共形场论)》各章之后有大量的练习题,可检验和加深对所学内容的理解。
《onformal Field Theory Vol.1(共形场论)》可作为高等院校理论物理和数学专业高年级本科生和研究生教材,也可供物理学和数学等相关学科研究人员参考。对于这些领域的研究人员和高校师生,这是一本不可多得的参考书。
目录
Preface
PartA INTRODUCTION
1 Introduction
2 Quantum Field Theory
2.1 Quantum Fields
2.1.1 The Free Boson
2.1.2 The Free Fermion
2.2 Path Integrals
2.2.1 System with One Degree of Freedom
2.2.2 Path Integration for Quantum Fields
2.3 Correlation Functions
2.3.1 System with One Degree of Freedom
2.3.2 The Euclidiall Formalism
2.3.3 The Generating Funcfional
2.3.4 Example:The Free Boson
2.3.5 Wick’S Theorem
2.4 Symmetries andConservationLaws
2.4.1 Continuous Symmetry Transformations
2.4.2 Infinitesimal Transformations and Noether's Theorem
2.4.3 Transformation of the Correlation Functions
2.4.4 Ward Identities
2.5.1 The Energy-Momentum Tensor
2.5.1 The Belinfante 1lensor
2.5.2 Alternate Definition of the Energy-Momentum Tensor
2.A Gaussian Integrals
2.B Grassmann Variables
2.C Tetrads
Exercises
3 Statistical Mechanics
3.1 11le Boltzmann Distribution
3.1.1 Classical Statistical Models
3.1.2 Quantum Statistics
3.2 Critical Phenomena
3.2.1 Generalities
3.2.2 Scaling
3.2.3 Broken Symmetry
3.3 The Renormalization Group:Lattice Models
3.3.1 Generalities
3.3.2 The Ising Model on a Triangular Lattice
3.4 The Renormalization Group:Continuum Models
3.4.1 Introduction
3.4.2 Dimensional Analysis
3.4.3 Beyond Dimensional Analysis:The φ4 Theory
3.5 The Transfer MaUix
Exercises
Part B FUNDAMENTALS
4 GIobal Conformal Invariance
4.1 The Conformal Group
4.2 Conformal Invariance in Classical Field Theory
4.2.1 Representations of the Conformal Group in d Dimensions
4.2.2 The Energy—Momentum Tensor
4.3 Conformal Invariance in Quantum Field Theory
4.3.1 Correlation Functions
4.3.2 Ward Identifies
4.3.3 Tracelessness of Tuv in Two Dimensions
Exercises
5 Conformai Invariance In Two Dimensions
5.1 The Conformal Group in Two Dimensions
5.1.1 Conformal Mappings
5.1.2 Global Conformal Transformations
5.1.3 Conformal Generators
5.1.4 Primary Fields
5.1.5 Correlation Funcfions
5.2 Ward Identities
5.2.1 HolomorphicFormoftheWardIdentities
5.2.2 The Conformal Ward Idcntity
5.2.3 Alternate Derivation of the Ward Identities
5.3 Free Fields and the Operator Product Expansion
5.3.1 The Free Boson
5.3.2 Tt Free Fermion
5.3.3 The Ghost System
5.4 the Central Charge
5.4.1 Transformation of the Energy-Momentum Tensor
5.4.2 Physical Meaning of C
5.A The Trace Anomaly
5.B The Heat Kemel
Exercises
6 The Operator Formalism
6.1 The Operator Formalism of Conformal Field Theory
6.1.1 Radial Quantization
6.1.2 Radial Ordering and Operator Product Expansion
6.2 The Virasoro Algebra
6.2.1 Conformal Generators
6.2.2 The Hilbert Space
6.3 The Free Boson
6.3.1 Canonical Quantization on the Cylinder
6.3.2 Vertex Operators
6.3.3 The Fock Space
6.3.4 Twitled Boundary Conditions
6.3.5 Compactified Boson
6.4 1 the Free Fermion
6.4.1 Canonical Quantization on a Cylinder
6.4.2 Mapping onto the Plane
6.4.3 Vacuum Energies
6.5 Nor mal Ordering
6.6 Conformal Families and Operator Algebra
6.6.1 Descendant Fields
6.6.2 Conformal Families
6.6.3 The Operator Algebra
6.6.4 Conformal Blocks
6.6.5 Crossing Symmetry and the Conformal Bootstrap
6.A Vertex and Coherent States
6.B The Generalized Wick Theorem
6.C A Rearrangement Lemma
6.D Summary of Important Formulas
Exercises
7 Minimal Modds I
7.1 verma Modules
7.1.1 Highest-Weight Representations
7.1.2 Virasoro Characters
7.1.3 Singular vectors and Reducible Verma Modules
7.2 the Kac Determinant
7.2.1 Unitarity and the Kac Determinant
7.2.2 Unitarity of C≥l Representations
7.2.3 Unitary C
7.3 overyiew of Minimal Models
7.3.1 A Simple Example
7.3.2 TnIncation of the Operator Algebra
7.3.3 Minimal Models
7.3.4 Unitary Minimal Models
7.4 ExampleS
7.4.1 The Yang—lee Singularity
7.4.2 The Ising Model
7.4.3 The Tricritical Ising Model
7.4.4 The Three—State Potts Model
7.4.5 RSOS Models
7.4.6 The O(n)Model
7.4.7 Effective Landau—Ginzburg Description of Unitary
Minimal Models Exercises
8 Minimal Models II
8.1 Irreducible Modules and Minimal Chacters
8.1.1 The Structure of Reducible Verma Modules forMinimal Models
8.1.2 Cllaracters
8.2 Explicit Form of Singular Vectors
8.3 Diffrential Equations for the Correlation Functions
8.3.1 From Singular Vectors to Differential Equations
8.3.2 Differential Equations for TwO-Point Functions in Minimal Models
8.3.3 Differential Equations for Fbu-Point Functions in Minimal Models
8.4 Fusion Rules
8.4.1 From Differential Equations to Fusion Rules
8.4.2 Fusion Algebra
8.4.3 Fusion Rules for the Minimal Models
8.A General Singular Vectors from the Covariance of theOPE
8.A.1 Fusion of Irreducible Modules and OPE Coefficients
8.A.2 The Fusion Map f:Transferring the Action ofOperators
……
9 The Coulomb-Gas Formalism
10 Modular Invariance
11 Finite-Size Scaling and Boundaries
12 The Two-Dimensional Ising Model
Part C CONFORMAL FIELD THEORIES WITH LIE-GROUP SYMMETRY
13 Simple Lie Algebras
14 Affine Lie Algebras
15 WZW Models
16 Fusion Rules in WZW Models
17 Modular Invariants in WZW Models
18 Cosets
References
Index
……[看更多目录]
序言所谓共形场论,就是共形群变换下不变的经典或量子场论。共形变换群是庞加莱群(Poincare Group)的推广。
共形场论(CFT)是过去20年里理论物理中最活跃且成果丰硕的研究领域之一。到目前为止,《Conformal Field Theory Vol.1(共形场论)》是第一部,也是唯一一部全面系统介绍共形场论的专著。
共形场论已经广泛应用于弦理论、统计物理、凝聚态物理和纯粹数学等诸多方面的研究。例如:弦的世界面(Worldsheet)所构成的黎曼面由二维共形场论来刻画;在数学理论中,如Borcherds(菲尔兹奖获得者)提出的顶点算子代数(Vertex Operator Algebra),即为二维共形场论的代数理论,Drinfeld(菲尔兹奖获得者)等提出的所谓手征代数(Chiral Algebra),则是试图从代数几何的观点理解二维共形场论。
《Conformal Field Theory Vol.1(共形场论)》共18章,分为3个部分。
第1部分——简介。第l章中对《Conformal Field Theory Vol.1(共形场论)》涉及的相关概念进行了简单回顾。第2章是量子场论的一些基本概念,如自由玻色(费米)子,路径积分,关联函数,对称与守恒量,以及能动张量。第3章则涉及统计力学的一些基本概念,如玻尔兹曼分布,临界现象,重整化群和转移矩阵。
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