David Yevick是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
目录
Preface
Preface to the Third Edition
General Sources and References
PARTⅠBASICIDEAS AND TECHNIQUES
1 Pertinent concepts and ideas in the theory of critical phenomena
1-1 Description of critical phenomena
1-2 Scaling and homogeneity
1-3 Comparison of various results for critical exponents
1-4 Universality-dimensionality，symmetry
Exercises
2 Formulation of the problem of phase transitions in terms of functional integrals
2-1 Introduction
2-2 Construction of the Lagrangian
2-2-1 The real scalar field
2-2-2 Complexfield
2-2-3 A hypercubic n-vector model
2-2-4 Two coupled fluctuating fields
2-3 The parameters appearing in ￡
2-4 The partition function，or the generating functional
2-5 Representation of the Ising model in terms of functional integrals
2-5-1 Definition of the model and its thermodynamics
2-5-2 The Gaussian transformation
2-5-3 The free part
2-5-4 Some properties of the free theory-a free Euclidean field theory in less than four dimensions
2-6 Correlation functions including composite operators
Exercises
3 Functional integrals in quanturn field theory
3-1 Introduction
3-2 Functionalintegrals for a quantum-mechanical system with one degree of freedom
3-2-1 Schwinger's transformation function
3-2-2 Matrix elements-Green functions
3-2-3 The generating functional
3-2-4 Analytic continuation in time-the Euclidean theory
3-3 Functional integrals for the scalar boson field theory
3-3-1 Introduction
3-3-2 The generating functional for Green functions
3-3-3 The generating functional as a functional integral
3-3-4 The S-matrix expressed in terms of the generating functional
Exercises
4 Perturbation theory and Feynman graphs
4-1 Introduction
4-2 Perturbation expansionin coordinate space
4-3 The cancellation of vacuum graphs
4-4 Rules for the computation ofgraphs
4-5 More general cases
4-5-1 The M-vector theory
4-5-2 Comments on fields with higher spin
4-6 Diagrammatic expansion in momentum space
4-7 Perturbation expansion of Green functions with composite operators
4-7-1 In coordinate space
4-7-2 In momentum space
4-7-3 Insertion at zero momentum
Exercises
5 Vertex functions and symmetry breaking
5-1 Introduction
5-2 Connected Green functions and their generating functional
5-3 The mass operator
5-4 The Legendre transform and vertex functions
5-5 The generating functional and the potential
5-6 Ward-Takahashi identities and Goldstone's theorem
5-7 Vertex parts for Green functions with composite operators
Exercises
6 Expansions in the number of loops and in the number of components
6-1 Introduction
6-2 The expansion in the number of loops as a power series
6-3 The tree （Landau-Ginzburg）approximation
6-4 The one-loop approximation and the Ginzburg criterion
6-5 Mass and coupling constant renormalizationin the one-loop approximation
6-6 Composite field renormalization
6-7 Renormalization of the field at the two-loop level
6-8 The 0（M）-symmetric theory in the limit of large M
6-8-1 Generalremarks
6-8-2 The origin of the M-dependence of the coupling constant
6-8-3 Faithful representation of graphs and the dominant terms inΓ（4）
6-8-4 Γ（2） in theinfinite M limit
6-8-5 Renormalization
6-8-6 Broken symmetry
Appendix 6-1 The method of steepest descent and the loop expansion
Exercises
7 Renormalization
7-1 Introduction
7-2 Some considerations concerning engineering dimensions
7-3 Power counting and primitive divergences
7-4 Renormalization of a cutoff φ4 theory
7-5 Normalization conditions for massive and massless theories
7-6 Renormalization constants for a massless theory to order two loops
7-7 Renormalization away from the critical point
7-8 Counterterms
7-9 Relevant and irrelevant operators
7-10 Renormalization of a φ4 theory with an 0（M） symmetry
7-11 Ward identities and renormalization
7-12 Iterative construction of counterterms
Exercises
8 The renormalization group and scaling in the critical region
8-1 Introduction
8-2 The renormalization group for the critical （massless） theory
8-3 Regularization by continuation in the number of dimensions
8-4 Massless theory below four dimensions-the emergence of ε
8-5 The solution of the renormalization group equation
8-6 Fixed points， scaling， and anomalous dimensions
8-7 The approach to the fixed point-asymptotic freedom
8-8 Renormalization group equation above Tc-identification of v
8-9 Below the critical temperature-the scaling form of the equation of state
8-10 The specific heat-renormalization group equation for an additively renormalized vertex
8-11 The Callan-Symanzik equations
8-12 Renormalization group equations for the bare theory
8-13 Renormalization group equations and scaling in the infinite M limit
Appendix 8-1 General formulas for calculating Feynman integrals
Exercises
9 The computation of the critical exponents
9-1 Introduction
9-2 The symbolic calculation of the renormalization constants and Wilson functions
9-3 The εexpansion of the critical exponents
9-4 The nature of the fixed points -universality
9-5 Scale invariance at finite cutoff
9-6 At the critical dimension -asymptotic infrared freedom
9-7 ε expansion for the Callan-Symanzik method
9-8 εexpansion of the renormalization group equations for the bare functions
9-9 Dimensional regularization and critical phenomena
9-10 Renormalization by minimal subtraction of dimensional poles
9-11 The calculation of exponents in minimal subtraction
Appendix 9-1 Calculation of some integrals with cutoff
9-2 One-Ioop integrals in dimensional regularization
9-3 Two-Ioop integrals in dimensional regularization
Exercises
……
PARTⅡ FURTHER APPLICATIONS AND DEVELOPMENTS
