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Index
Title Page
Preface
Acknowledgements
Notations and Conventions
Foreword
Part I - Feynman Diagrams and Quantum Electrodynamics
Chapter 1 - Invitation: Pair Production in ee Annihilation
The Simplest Situation
Embellishments and Questions
Chapter 2 - The Klein-Gordon Field
2.1 The Necessity of the Field Viewpoint
2.2 Elements of Classical Field Theory
2.3 The Klein-Gordon Field as Harmonic Oscillators
2.4 The Klein-Gordon Field in Space-Time
Problems
Chapter 3 - The Dirac Field
3.1 Lorentz Invariance in Wave Equations
3.2 The Dirac Equation
3.3 Free-Particle Solutions of the Dirac Equation
3.4 Dirac Matrices and Dirac Field Bilinears
3.5 Quantization of the Dirac Field
3.6 Discrete Symmetries of the Dirac Theory
Problems
Chapter 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
4.8 Feynman Rules for Quantum Electrodynamics
Problems
Chapter 5 - Elementary Processes of Quantum Electrodynamics
5.1 ee → µµ: Introduction
5.2 ee → μμ: Helicity Structure
5.3 ee → μμ: Nonrelativistic Limit
5.4 Crossing Symmetry - Electron-Muon Scattering
5.5 Compton Scattering
Problems
Chapter 6 - Radiative Corrections: Introduction
6.1 Soft Bremsstrahlung
6.2 The Electron Vertex Function: Formal Structure
6.3 The Electron Vertex Function: Evaluation
16.4 The Electron Vertex Function: Infrared Divergence
6.5 Summation and Interpretation of Infrared Divergences
Problems
Chapter 7 - Radiative Corrections: Some Formal Developments
7.1 Field-Strength Renormalization
7.2 The LSZ Reduction Formula
7.3 The Optical Theorem
7.4 The Ward-Takahashi Identity
7.5 Renormalization of the Electric Charge
Problems
Final Project - Radiation of Gluon Jets
Part II - Renormalization
Chapter 8 - Invitation: Ultraviolet Cutoffs and Critical Fluctuations
Formal and Physical Cutoffs
Landau Theory of Phase Transitions
Critical Exponents
Chapter 9 - Functional Methods
9.1 Path Integrals in Quantum Mechanics
9.2 Functional Quantization of Scalar Fields
9.3 The Analogy Between Quantum Field Theory and Statistical Mechanics
9.4 Quantization of the Electromagnetic Field
9.5 Functional Quantization of Spinor Fields
9.6 Symmetries in the Functional Formalism
Problems
Chapter 10 - Systematics of Renormalization
10.1 Counting of Ultraviolet Divergences
10.2 Renormalized Perturbation Theory
10.3 Renormalization of Quantum Electrodynamics
10.4 Renormalization Beyond the Leading Order
10.5 A Two-Loop Example
Problems
Chapter 11 - Renormalization and Symmetry
11.1 Spontaneous Symmetry Breaking
11.2 Renormalization and Symmetry: An Explicit Example
11.3 The Effective Action
11.4 Computation of the Effective Action
11.5 The Effective Action as a Generating Functional
11.6 Renormalization and Symmetry: General Analysis
Problems
Chapter 12 - The Renormalization Group
12.1 Wilson’s Approach to Renormalization Theory
12.2 The Callan-Symanzik Equation
12.3 Evolution of Coupling Constants
12.4 Renormalization of Local Operators
12.5 Evolution of Mass Parameters
Problems
Chapter 13 - Critical Exponents and Scalar Field Theory
13.1 Theory of Critical Exponents
13.2 Critical Behavior in Four Dimensions
13.3 The Nonlinear Sigma Model
Problems
Part III - Non-Abelian Gauge Theories
Chapter 14 - Invitation: The Parton Model of Hadron Structure
Almost Free Partons
Asymptotically Free Partons
Chapter 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
Problems
Chapter 16 - Quantization of Non-Abelian Gauge Theories
16.1 Interactions of Non-Abelian Gauge Bosons
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
16.6 Asymptotic Freedom: The Background Field Method
16.7 Asymptotic Freedom: A Qualitative Explanation
Problems
Chapter 17 - Quantum Chromodynamics
17.1 From Quarks to QCD
17.2 ee Annihilation into Hadrons
17.3 Deep Inelastic Scattering
17.4 Hard-Scattering Processes in Hadron Collisions
17.5 Parton Evolution
17.6 Measurements of α
Problems
Chapter 18 - Operator Products and Effective Vertices
18.1 Renormalization of the Quark Mass Parameter
18.2 QCD Renormalization of the Weak Interaction
18.3 The Operator Product Expansion
18.4 Operator Analysis of ee Annihilation
18.5 Operator Analysis of Deep Inelastic Scattering
Problems
Chapter 19 - Perturbation Theory Anomalies
19.1 The Axial Current in Two Dimensions
19.2 The Axial Current in Four Dimensions
19.3 Goldstone Bosons and Chiral Symmetries in QCD
19.4 Chiral Anomalies and Chiral Gauge Theories
19.5 Anomalous Breaking of Scale Invariance
Problems
Chapter 20 - Gauge Theories with Spontaneous Symmetry Breaking
20.1 The Higgs Mechanism
20.2 The Glashow-Weinberg-Salam Theory of Weak Interactions
20.3 Symmetries of the Theory of Quarks and Leptons
Problems
Chapter 21 - Quantization of Spontaneously Broken Gauge Theories
21.1 The R Gauges
21.2 The Goldstone Boson Equivalence Theorem
21.3 One-Loop Corrections to the Weak-Interaction Gauge Theory
Problems
Final Project
Epilogue
Appendix - Reference Formulae
Bibliography
Index
Copyright Page
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