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 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
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