共形場論第1卷

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
　　……
　6 The Operator Formalism
　7 Minimal Models Ⅰ
　8 Minimal Models Ⅱ
　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