作者：Philippe Di Francesc
页数：21,486页
出版社：世界图书出版公司
出版日期：2009
ISBN：9787506292610
电子书格式：pdf/epub/txt
内容简介
共形场论(CFT)是过去几十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，本书是第一部，也是一部全面系统介绍共形场论的专著。本书原版共18章，分为3个部分。世图引进的英文版将其分成了两卷。
第1卷各章主要内容：（一）简介：第1章中对本书涉及的相关概念进行了简单回顾，第2章介绍量子场论的一些基本概念，第3章则涉及统计力学的一些基本概念。（二）基础理论：第4章介绍了全局的共形不变，第5章详细论述了有关二维共形不变基本而重要的概念，第6章则是更为详细论述算子表述下的共形场论，随后两章论述了极小模型，第9~10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2卷目次:（三）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，第14章为仿射李代数，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，第18章为陪集构造。陪集构造是共形场论最重要的手段之一。本书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。
本书特色
本书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。
目录
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 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
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 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
