导语

  

内容提要

  

    《量子场论导论》是物理学研究生课程的一本教科书，内容涵盖相对论量子力学、量子电动力学和费曼图。作者通过精心设计的例子，说明了这些科目的技术方面，并直观地解释了数学背后发生的事情，从而使这门课易于理解。在介绍量子电动力学的基础上，讨论了重正化理论及其与统计力学的关系，并引入了重正化群。这一讨论为讨论构成基本粒子物理基本相互作用基础的物理原理及其用规范场理论的描述奠定了基础。

Preface
Notations and Conventions
Editor's Foreword
Part IⅠ: Feynman Diagrams and Quantum Electrodynamics
  1  Invitation: Pair Production in e+e- Annihilation
  2  The Klein-Gordon Field
    2.1  The Necessity of the Field Viewpoint
    2.2  Elements of Classical Field Theory
      Lagrangian Field Theory; Hamiltonian Field Theory; Noether's Theorem
    2.3  The Klein-Gordon Field as Harmonic Oscillators
    2.4  The Klein-Gordon Field in Space-Time
      Causality; The Klein-Gordon Propagator; Particle Creation by a Classical Source Problems
  3  The Dirac Field
    3.1  Lorentz Invariance in Wave Equations
    3.2  The Dirac Equation
      Weyl Spinors
    3.3  Free-Particle Solutions of the Dirac Equation
      Spin Sums
    3.4  Dirac Matrices and Dirac Field Bilinears
    3.5  Quantization of the Dirac Field
      Spin and Statistics; The Dirac Propagator
    3.6  Discrete Symmetries of the Dirac Theory
      Parity; Time Reversal; Charge Conjugation Problems
  4  Interacting Fields and Feynman Diagrams
    4.1  Perturbation Theory-Philosophy and Examples
    4.2  Perturbation Expansion of Correlation Functions
    4.3  Wick's Theorem
    4.4  Feynman Diagrams
    4.5  Cross Sections and the S-Matrix
    4.6  Computing S-Matrix Elements from Feynman Diagrams
    4.7  Feynman Rules for Fermions
      Yukawa Theory
    4.8  Feynman Rules for Quantum Electrodynamics
      The Coulomb Potential Problems
  5  Elementary Processes of Quantum Electrodynamics
    5.1  e+e- → μ+μ-: Introduction
      Trace Technology; Unpolarized Cross Section; e+e- → Hadrons
    5.2  e+e- → μ+μ-: Helicity Structure
    5.3  e+e- → μ+μ-: Nonrelativistic Limit
      Bound States; Vector Meson Production and Decay
    5.4  Crossing Symmetry
      Electron-Muon Scattering; Mandelstam Variables
    5.5  Compton Scattering
      Photon Polarization Sums; The Klein-Nishina Formula; High-Energy Behavior; Pair Annihilation into Photons Problems
  6  Radiative Corrections: Introduction
    6.1  Soft Bremstrahlung
      Classical Computation; Quantum Computation
    6.2  The Electron Vertex Function: Formal Structure
    6.3  The Electron Vertex Function: Evaluation
      Feynman Parameters; Precision Tests of QED
    6.4  The Electron Vertex Function: Infrared Divergence
    *6.5  Summation and Interpretation of Infrared Divergences
      Problems
  7  Radiative Corrections: Some Formal Developments
    7.1  Field-Strength Renormalization
      The Electron Self-Energy
    7.2  The LSZ Reduction Formula
    7.3  The Optical Theorem
      The Optical Theorem for Feynman Diagrams; Unstable Particles
    7.4  The Ward-Takahashi Identity
    7.5  Renormalization of the Electric Charge
      Dimensional Regularization
      Problems
  Final Project: Radiation of Gluon Jets
Part Ⅱ: Renormalization
  8  Invitation: Ultraviolet Cutoffs and Critical Fluctuations
  9  Functional Methods
    9.1  Path Integrals in Quantum Mechanics
    9.2  Functional Quantization of Scalar Fields
      Correlation Functions; Feynman Rules; Functional Derivatives and the Generating Functional
    9.3  Quantum Field Theory and Statistical Mechanics
    9.4  Quantization of the Electromagnetic Field
    9.5  Functional Quantization of Spinor Fields
      Anticommuting Numbers; The Dirac Propagator; Generating Functional for the Dirac Field; QED; Functional Determinants
    *9.6  Symmetries in the Functional Formalism
      Equations of Motion; Conservation Laws; The Ward-Takahashi Identity
      Problems
  10  Systematics of Renormalization
    10.1  Counting of Ultraviolet Divergences
    10.2  Renormalized Perturbation Theory
      One-Loop Structure of φ4 Theory
    10.3  Renormalization of Quantum Electrodynamics
      One-Loop Structure of QED
    10.4  Renormalization Beyond the Leading Order
    *10.5  A Two-Loop Example
      Problems
  11  Renormalization and Symmetry
    11.1  Spontaneous Symmetry Breaking
      The Linear Sigma Model; Goldstone's Theorem
    *11.2  Renormalization and Symmetry: An Explicit Example
    *11.3  The Effective Action
    *11.4  Computation of the Effective Action
      The Efective Action in the Linear Sigma Model
    *11.5  The Effective Action as a Generating Functional
    *11.6  Renormalization and Symmetry: General Analysis
      Goldstone's Theorem Revisited
      Problems
  12  The Renormalization Group
    12.1  Wilson's Approach to Renormalization Theory
    12.2  The Callan-Symanzik Equation
      Renormalization Conditions; The Callan-Symanzik Equation; Computation of β and γ; The Meaning of β and γ
    12.3  Evolution of Coupling Constants
      Solution of the Callan-Symanzik Equation; An Application to QED; Alternatives for the Running of Coupling Constants
    *12.4  Renormalization of Local Operators
    *12.5  Evolution of Mass Parameters
      Critical Exponents: A First Look Problems
  13  Critical Exponents and Scalar Field Theory
    *13.1  Theory of Critical Exponents
      Exponents of the Spin Corelation Function; Exponents of Thermodynamic Functions; Values of the Critical Exponents
    *13.2  Critical Behavior in Four Dimensions
    *13.3  The Nonlinear Sigma Model
      Problems
  Final Project: The Coleman-Weinberg Potential
Part Ⅲ: Non-Abelian Gauge Theories
  14  Invitation: The Parton Model of Hadron Structure
  15  Non-Abelian Gauge Invariance
    15.1  The Geometry of Gauge Invariance
    15.2  The Yang-Mills Lagrangian
    *15.3  The Gauge-Invariant Wilson Loop
    15.4  Basic Facts About Lie Algebras
      Clasification of Lie Algebras; Representations; The Casimir Operator Problems
  16  Quantization of Non-Abelian Gauge Theories
    16.1  Interactions of Non-Abelian Gauge Bosons
      Feynman Rules for Fermions and Gauge Bosons; Equality of Coupling Constants; A Flaw in the Argument
    16.2  The Faddeev-Popov Lagrangian
    16.3  Ghosts and Unitarity
    *16.4  BRST Symmetry
    *16.5  One-Loop Divergences of Non-Abelian Gauge Theory
      The Gauge Boson Self-Energy; The β Function; Relations among Counterterms
    *16.6  Asymptotic Freedom: The Background Field Method
    16.7  Asymptotic Freedom: A Qualitative Explanation
      Problems
  17  Quantum Chromodynamics
    17.1  From Quarks to QCD
    17.2  e+e- Annihilation into Hadrons
      Total Cross Section; The Running of as; Gluon Emission
    17.3  Deep Inelastic Scattering
      Deep Inelastic Neutrino Scattering; The Distribution Functions
    17.4  Hard-Scattering Processes in Hadron Collisions
      Lepton Pair Production; Kinematics; Jet Pair Production
    17.5  Parton Evolution
      The Equivalent Photon Approximation; Multiple Splittings; Evolution Equations for QBD; The Altarelli-Parisi Equations
    17.6  Measurements of αs
      Problems
  18  Operator Products and Effective Vertices
    *18.1  Renormalization of the Quark Mass Parameter
    *18.2  QCD Renormalization of the Weak Interactions
    *18.3  The Operator Product Expansion
    *18.4  Operator Analysis of ete-Annihilation
    *18.5  Operator Analysis of Deep Inelastic Scattering
      Kinematics; Expansion of the Operator Product; The Dispersion Integral; Operator Rescaling; Operator Mixing; Relation to the Altarelli-Parisi Equations Problems
  19  Perturbation Theory Anomalies
    *19.1  The Axial Current in Two Dimensions
      Vacuum Polarization Diagrams; The Current Operator Equation; An Example with Fermion Number Nonconservation
    *19.2  The Axial Current in Four Dimensions
      The Current Operator Equation; Triangle Diagrams; Chiral Transformation of the Functional Integral
    *19.3  Goldstone Bosons and Chiral Symmetries in QCD
      Spontaneous Breaking of Chiral Symmetry; Anomalies of Chiral Currents
    *19.4  Chiral Anomalies and Chiral Gauge Theories
    *19.5  Anomalous Breaking of Scale Invariance
      Problems
  20  Gauge Theories with Spontaneous Symmetry Breaking
    20.1  The Higgs Mechanism
      An Abelian Example; Systematics of the Higgs Mechanism; Non-Abelian Examples; Formal Description
    20.2  The Glashow-Weinberg-Salam Theory of Weak Interactions
      Gauge Boson Masses; Coupling to Fermions; Experimental Consequences of the Glashow-Weinberg-Salam Theory; Fermion Mass Terms; The Higgs Boson; A Higgs Sector?
    *20.3  Symmetries of the Theory of Quarks and Leptons
      Problems
  21  Quantization of Spontaneously Broken Gauge Theories
    21.1  The Re Gauges
      An Abelian Example; Dependence in Perturbation Theory; Non-Abelian Analysis
    21.2  The Goldstone Boson Equivalence Theorem
      Formal Aspects of Goldstone Boson Equivalence; Top Quark Decay; e+e- → W+W-
    *21.3  One-Loop Corections in Weak-Interaction Gauge Theory
      Theoretical Orientation, and a Specific Problem; Influence of Heavy Quark Corrections; Computation of Vacuum Polarization Amplitudes; The Efect of mt Problems
  Final Project: Decays of the Higgs Boson
Epilogue
  22  Quantum Field Theory at the Frontier
    22.1  Strong Strong Interactions
    22.2  Grand Unification and its Paradoxes
    22.3  Exact Solutions in Quantum Field Theory
    22.4  Supersymmetry
    22.5  Toward an Ultimate Theory of Nature
Appendix: Reference Formulae
  A.1  Feynman Rules
  A.2  Polarizations of External Particles
  A.3  Numerator Algebra
  A.4  Loop Integrals and Dimensional Regularization
  A.5  Cross Sections and Decay Rates
  A.6  Physical Constants and Conversion Factors
Bibliography
Index