Contents

• Introduction and Background
  • Introduction
  • Notation and Conventions
    • Units
    • Maxwell's Equations in Vacuum
    • Coordinates
    • Metric Tensor
    • Covariant and Contravariant Indices
    • 3-Vector, 4-Vector, and Scalar Product
    • Classification of 4-Vectors
    • Gradient and Differential Operators
    • Pauli Matrices
    • Useful Definitions
    • Problems
  • Lorentz Covariance
    • Lorentz Group
    • Lorentz Boost
    • Working Rules for Lorentz Covariance
  
  
• Relativistic Quantum Mechanics
  • Klein-Gordon Equation
    • Wave Equation for a Spin-0 Particle
    • Lorentz Invariance
    • Solutions of the Klein-Gordon Equation
    • General Solution of the Klein-Gordon Equation
    • Conserved Current and Charge
      • Charge of a Klein-Gordon Particle
    • Orthogonality and Normalization
    • Interaction with the Electromagnetic Field
      • Gauge Invariance
      • Electromagnetic Coupling
      • Charge Conjugation
    • Klein-Gordon Equation in Schrödinger Form
    • Zitterbewegung
    • Klein Paradox for Spin-0 Particles
    • Coulomb Interaction
    • Homogeneous Green Function
    • Completeness
    • Summary
    • Problems
  • Dirac Equation
    • Wave Equation for a Spin-1/2 Particle
    • Current Conservation
    • Dirac Particle at Rest
    • Electromagnetic Interaction
    • Nonrelativistic Limit of the Dirac Equation
    • Constants of the Motion
    • Free Motion of a Dirac Particle
    • Covariant Form of the Dirac Equation
    • Proof of Covariance
      • Rotations
      • Lorentz Boosts
      • Spatial Inversion
    • Covariance of the Continuity Equation
    • Adjoint Spinor
    • Bilinear Covariants
    • Plane-Wave Solutions
      • Spin
    • Projection Operators for Energy and Spin
      • Energy Projection Operators
      • Spin Projection Operators
      • Projection Operators of Energy and Spin
    • Hole Theory
    • Charge Conjugation
    • Time Reversal
    • Combined PCT Symmetry
    • Free-Particle Solutions and Wave Packets
    • Klein Paradox for Spin-1/2 Particles
    • Problems
  
  
• Quantum Electrodynamics
  • Propagator Methods
    • Green's Functions
    • Propagator Theory
    • The Nonrelativistic Propagator
    • Propagator in Relativistic Theory
    • Propagator for the Klein-Gordon Equation
    • Propagator for the Dirac Equation
    • S-Matrix
      • Electron Scattering
      • Pair Creation
      • Pair Annihilation
      • Positron Scattering
    • Problems
  • QED Processes
    • Lifetimes and Cross-Sections
    • Coulomb Scattering of Electrons
      • Trace Theorems
    • Coulomb Scattering of Positrons
    • Photons
      • Polarization Vectors
      • The Photon Propagator
    • The Substitution Rules
    • Lorentz-Invariant Phase Space
    • Electron Scattering from a Dirac Proton (the effect of recoil
    • Bremsstrahlung
    • Photon-Electron Scattering
    • Pair Annihilation into Gamma Rays
    • Pair Production
    • Electron-Electron Scattering
    • Electron-Positron Scattering
    • Polarization in Electron Scattering
    • Higher-Order Calculations: Tree and Loops
    • Feynman Rules for Tree Graphs
      • External Particles
      • Propagators
      • Vertices
    • Problems
  
  
• Appendices
  • Trace Calculation Using FORM
  
  
• Bibliography
• Index
• About this document ...