经典名著系列 共形场论 第2卷 英文版 作者： (法)菲利普迪弗朗切斯科 著 出版时间：2009年版 内容简介 《onformal Field Theory Vol.2(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.2(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.2(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。 目录 8.A.3 The Singular Vectors |hr，s+rs”>：General Strategy 8.A.4，the Leading ActionofA△ r，1 8.A.5 Fusion at Work 8.A.6 The Singular Vectors |hr，s+rs>：Summary Exercises
9 The Coulomb-Gas Formalism 9.1 Vertex Operators 9.1.1 Corrclators of Vertex Operators 9.1.2 the Neutrality Condition 9.1.3 the Back ground Charge 9.1.4 the AnomalOUS OPES 9.2 Screening Operators 9.2.1 Physical and Vertex Operators 9.2.2 Minimal Models 9.2.3 Four-POint Functions：Sample Correlators 9.3 Minimal Models：General Structure of Correlation Functions 9.3.1 Conformal Blocks for the Four-Point Functions 9.3.2 Conformal Blocks for the N-Point Function on the Plane 9.3.3 Monodromy and Exchange Relations for Conformal Blocks 9.3.4 Conformal Blocks for Corrclators on a Surface of Arbitrary Genus 9.A Calculation of the Energy-Momentum Tensor 9.B Screened Vertex Operators and BRST Cohomology：A Proof of the Coulomb-Gas Representation Of Minimal Models 9.B.1 Charged Bosonic Fock Spaces and Their Virasoro Structure 9.B.2 Screened Vertex Operators 9.B.3 The BRST Charge 9.B.4 BRST Invariance and Cohomology 9.B.5 The Coulomb-Gas Representation Exercises
10 Modular Invariance 10.1 C0nformal Field Theory on the Torus 10.1.1 The Partition Function 10.1.2 Modular Invariance 10.1.3 Generators and the Fundamental Domain 10.2 The Free Boson on the Torus 10.3 Free Fermions on the Torus 10.4 Models with C=1 10.4.1 Compactified Boson 10.4.2 Multi-Component Chiral Boson 10.4.3 Orbifold 10.5 Minimal Models：Modular Invariance and operater Content 10.6 Minimal Models：Modular Transformations of the Characters
10.7 MinimaI Models：Modular lnvariant Partition Funcfions 10.7.1 Diagonal Modular Invariants 10.7.2 Nondiagonal Modular Invariants：Example of the Three-state Potts Model 10.7.3 Block-Diagonal Modular Invariants 10.7.4 Nondiagonal Modular Invariants Related to an Automorphism 10.7.5 D Seriesfrom Z2 OrbifoldS 10.7.6 The Classification of Minimal Models
10.8 Fusion Rules and Modular Invariance 10.8.1 verlindeS Formula for Minimal Theories 10.8.2 Counting Conformal Blocks 10.8.3 A General Proof of Verlindes Formula 10.8.4 Extended Symmetries and Fusion Rules 10.8.5 Fusion Rules of the Extended Theory of the Three-State Potts Model 10.8.6 A Simple Example of Nonminimal Extended Theory：The Free Boson at the Self-Dual Radius 10.8.7 Rational Conformal Field Theory：A Definition 10.A Theta Functions 10.A.1 The Jacobi Tripie Product 10.A.2 Theta Functions 10.A.3 DedekindS n Funcfion 10.A.4 Modular Transformations of Theta Functions 10.A.5 Doubling Identities Exercises
11 Finite-Size Scaling and Boundaries 11.1 Conformal Invariance on a Cylinder 11.2 Surface Critical Behavior 11.2.1 Conforrnal Field rnleory on the Upper Half-Plane 11.2.2 The Ising Model on the Upper Half-Plane 11.2.3 The Infinite Strip
11.3 Boundary Operators 11.3.1 Introduction 11.3.2 Boundary States and the Verlinde Formula
11.4 Critical Percolation 11.4.1 Statement of the Problem 11.4.2 Bond Percolation and the Q-state POtts Model 11.4.3 Boundary Operators and Crossing Probabilities Exercises
12 The Two-Dimensional Ising Modd 12.1 The Statistical Model 12.2 The Underlying Fermionic Theory 12.2.1 Fermion：Energy and Energy-Momentum Tensor 12.2.2 Spin
12.3 Correlation Functions on the Plane by Bosonization 12.3.1 the Bosonization Rules 12.3.2 Energy Correlators 12.3.3 Spin and General Correlators
12.4 The Ising Model on the Torus 12.4.1 The Partition Function 12.4.2 General Ward Identifies on the Torus
12.5 Correlation Functions on the Torus 12.5.1 Flermion and Energy Correlators 12.5.2 Spin and Disorder-Field Correlators
12.6 Bosonization on the Torus 12.6.1 The Tw0 Bosonizations of the Ising Model：Partition Functions and Operators 12.6.2 Compactified Boson Correlations on the Plane and or the Torus 12.6.3 Ising Correlators from the Bosonization of the Dirac Fermion 12.6.4 Ising Correlators from the Bosonization of Two Real Fermions 12.A Elliptic and Treta Function Identities 12.A.1 Generalities on Elliptic Functions 12.A.2 Periodicity and ZeroS of the Jacobi Theta Functions 12.A.3 Doubling Identifies Exercises Part C CONOFRMAL FIELD THEORIES WITH LIE-GROUP SYMMETRY
13 Simple Lie Algebras 13.1 The Structure of Simple Lie Algebras 13.1.1 TheCartan-Wevl Basis 13.1.2 The Killing Form 13.1.3 Weigllts 13.1.4 Simple Roots and the Caftan Matrix 13.1.5 The Chevalley Basis 13.1.6 Dynkin Diagrams 13.1.7 Fundamental Weights 13.1.8 TheWeyl Group 13.1.9 Lattices 13.1.10 Normalization Convention 13.1.11 Examples
13.2 Highest-Weight Representations 13.2.1 Weights and Their Multiplicities l3.2.2 Conjugate Representations 13.2.3 Quadratic Casimir Operator 13.2.4 Index of a Representation
13.3 Tableaux and Patterns (su(N)) 13.3.1 Young Tableaux 13.3.2 Partitions and Orthonormal Bases 13.3.3 Semistandard Tableaux 13.3.4 Gelfand-Tsetlin Paaerns
13.4 Characters 13.4.1 WleylS Character Formula 13.4.2 The Dimension and the Strange Formulae 13.4.3 Schur Functions
13.5 Tensor Products：Computational Tools 13.5.1 The Character Method 13.5.2 Algorithm for the Calculation of Tensor Products 13.5.3 The Littlewood-Rchardson Rule 13.5.4 Berenstein-Zelevinsky Triangles 13.6 Tensor Products：A Fusion-Rule Point of View
13.7 Algebra Embeddings and Branching Rules 13.7.1 Embedding Index 13.7.2 Classification of Embeddings 13.A Properties of Simple Lie Algebras 13.B Notation for Simple Lie Algebras Exercises
14 Affine Lie Algebras 14.1 The Structure Of AfIine Lie Algebras 14.1.1 From Simple Lie Algebras to Affine Lie Algebras 14.1.2 The killing Form 14.1.3 Simple Roots，the Cartan Matrix and Dynkin Diagrams 14.1.4 The ChevalIcy Basis 14.1.5 Fundamental Weights 14.1.6 The Affine Weyl Group 14.1.7 Examples
14.2 Outer Automorphisms 14.2.1 Symmetry of the Extended Diagram and Group of Outer Auto morphisms 14.2.2 Action of Outer Automorphisms on Wleights …… 15 WZW Models 16 Fusion Rules in WZW Models 17 Modular Invariants in WZW Models 18 Cosets References Index
