Preface Part A 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 Euclidian Formalism 2.3.3 The Generating Functional 2.3.4 Example: The Free Boson 2.3.5 Wick's Theorem 2.4 Symmetries and Conservation Laws 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 The Energy-Momentum Tensor 2.5.1 The Belinfante Tensor 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 The 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 o4 Theory 3.5 The Transfer Matrix Exercises Part B FUNDAMENTALS 4 Global 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 Identities 4.3.3 Tracelessness of Tuv in Two Dimensions Exercises 5 Conformal 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 Functions ���� 6 The Operator Formalism 7 Minimal Models �� 8 Minimal Models �� 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