依据通行的观点，物质的基本彻块是夸克与轻子，它们通过杨-米尔斯规范场的媒介相互作用(在这种场合下引力被忽略了)。这就意味着相互作用的形式是完全由某些内部对称群的代数结构所决定的。于是强相互作用是与SU(3)群相关联的，它是由叫做量子色动力学的规范场理论所描述的。而电一弱相互作用则是与SU(2)XU(1)群相关联的，现在它是由标准的温伯格-萨拉姆模型来描述的。本书简明地介绍了在这些思想背后的动力，以及由此而来的严谨的数学系统表述。

PREFACE

I.INTRODUCTION

 1.1 Particles and Interactions

 1.2 Gauge Theories of Interactions

 1.3 Notations and Conventions

II.QUARKS

 2.1 Internal Symmetries

1 Isospin

2 The gauge groups

3 More general internal symmetries: SU(n)

4 Unitary symmetry

 2.2 Representation of SU(3)

1 The basic representation

2 Young's tableaux

3 Irreducible representations

 2.3 The Quark Model

1 Quarks as basic triplets

2 Quarks as building blocks

3 Weight diagrams

4 The composition of hadrons

 2.4 Color

1 Independent quark model

2 Color SU(3) group

 2.5 Electromagnetic and Weak Probes

1 Electromagnetic interactions

2 Parton model

3 Evidence for color

4 Weak interactions

 2.6 Charm

1 The charmed quark

2 The J/φ and its family

3 Correspondence between quarks and leptons

III.MAXWELL FIELD: U(I) GAUGE THEORY

 3.1 Global and Local Gauge Invariance

 3.2 Spontaneous Breaking of Global Gauge Invariance: Goldstone Mode

 3.3 Spontaneous Breaking of Local Gauge Invariance: Higgs Mode

 3.4 Classical Finite-Energy Solutions

 3.5 Magnetic Flux Quantization

 3.6 Soliton Solutions: Vortex Lines

IV. YANG-MILLS FIELDS: NON-ABELIAN GAUGE THEORIES

 4.1 Introductory Note

 4.2 Lie Groups

1 Structure constants

2 Matrix representations

3 Topological properties

4 General remarks

 4.3 The Yang-Mills Constructions

1 Global gauge invariance

2 Local gauge invariance

 4.4 Properties of Yang-Milis Fields

1 Electric and magnetic fields

2 Dual tensor

3 Path representation of the gauge group

 4.5 Canonical Formalism

1 Equations of motion

2 Hamiltonian

 4.6 Spontaneous Symmetry Breaking

1 The little group

2 Higgs mechanism

V.TOPOLOGICAL SOLITONS

 5.1 Solitons

 5.2 The Instanton

1 Topological charge

2 Explicit solution

 5.3 The Monopole

1 Topological stability

2 Flux quantization

3 Boundary conditions

4 Explicit solution

5 Physical fields

6 Spin from isospin

VI.WEINBERG-SALAM MODEL

 6.1 The Matter Fields

 6.2 The Gauge Fields

1 Gauging SU(2)×U(1)

2 Determination of constants

3 Interactions

 6.3 The General Theory

1 Mass terms

2 Cabibbo angle

3 Kobayashi-Maskawa matrix

4 Solitons

VII.METHOD OF PATH INTEGRALS

 7.1 Non-Relativistic Quantum Mechanics

 7.2 Quantum Field Theory

 7.3 External Sources

 7.4 Euclidean 4-Space

 7.5 Calculation of Path Integrals

 7.6 The Feynman .Propagator

 7.7 Feynman Graphs

 7.8 Boson Loops and Fermion Loops

 7.9 Fermion Fields

VIII.QUANTIZATION OF GAUGE FIELDS

 8.1 Canonical Quantization

1 Free Maxwell field

2 Pure Yang-Mills fields

 8.2 Path Integral Method in Hamiltonian Form

 8.3 Feynman Path Integral: Fadeev-Popov Method

 8.4 Free Maxwell Field

1 Lorentz gauge

2 Coulomb gauge

3 Temporal and axial gauges

 8.5 Pure Yang-Mills Fields

I Axial gauge

2 Lorentz gauge: Fadeev-Popov ghosts

 8.6 The 0-World and the Instanton

1 Discovering the 0-world

2 lnstanton as tunneling solution

3 The 0-action

 8.7 Gribov Ambiguity

 8.8 Projection Operator for Gauss' Law

IX.RENORMALIZATION

 9.1 Charge Renormalization

 9.2 Perturbative Renormalization in Quantum Electredynamics

 9.3 The Renormalization Group

1 Scale transformations

2 Scaling form

3 Fixed points

4 Callan-Symanzik equation

 9.4 Scalar Fields

1 Renormalizability

2 Φ4 theory

3 "Triviality" and the Landau ghost

 9.5 The Physics of Renormalization

1 Renormalization-group transformation

2 Real-space renormalization

3 Fixed points and relevancy

4 Renormalization and universality

 Appendix to Chapter 9. Renormalization of QED

1 Vertex

2 Electron Propagator

3 Photon Propagator

4 Scaling Properties

5 Renormalization

6 Gauge Invariance and the Photon Mass

X.METHOD OF EFFECTIVE POTENTIAL

 10.1 Spontaneous Symmetry Breaking

 10.2 The Effective Action

 10.3 The Effective Potential

 10.4 The Loop Expansion

 10.5 One-Loop Effective Potential

 10.6 Renormalization

1 General scheme

2 Massive case

3 Massless case

 10.7 Dimensional Transmutation

 10.8 A Non-Relativistic Example

 10.9 Application to Weinberg-Salam Model

XI. THE AXIAL ANOMALY

 11.1 Origin of the Axial Anomaly

 11.2 The Triangle Graph

 11.3 Anomalous Divergence of the Chiral Current

 11.4 Physical Explanation of the Axial Anomaly

 11.5 Cancellation of Anomalies

 11.6 't Hooft's Principle

XII. QUANTUM CHROMODYNAMICS

 12.1 General Properties

1 Lagrangian density

2 Feynman rules

3 Quark-gluon interactions

4 Gluon self-interactions

 12.2 The Color Gyromagnetic Ratio

 12.3 Asymptotic Freedom

1 The running coupling constant

2 The vacuum as magnetic medium

3 The Nielsen-Hughes formula

 12.4 The Pion as Goldstone Boson

1 The low-energy domain

2 Chiral symmetry: an idealized limit

3 PCAC

4 The decay π0→2y

5 Extension to pion octet

 12.5 The U(1) Puzzle

 12.6 θ-Worlds in QCD

1 Euclidean action

2 The axial anomaly and the index theorem

3 Chiral limit: Collapse of the 0-worlds

4 Quark mass matrix

5 Strong CP violation

XIII. LATTICE GAUGE THEORY

 13.1 Wilson's Lattice Action

 13.2 Transfer Matrix

 13.3 Lattice Hamiltonian

 13.4 Lattice Fermions

 13.5 Wilson Loop and Confinement

 13.6 Continuum Limit

 13.7 Monte Carlo Methods

XIV. QUARK CONFINEMENT

 14.1 Wilson Criterion and Electric Confmement

 14.2 String Model of Hadrons

 14.3 Superconductivity: Magnetic Confinement

1 Experimental manifestation

2 Theory

3 Mechanism for monopole confinement

 14.4 Electric and Magnetic Order Parameters

 14.5 Scenario for Quark Confinement

 Appendix to Chapter 14.Symmetry and Confinement

1 Quark Propagator

2 Center Symmetry

3 Confinement as Symmetry

INDEX