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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 ...

 

Douglas M. Gingrich (gingrich@ ualberta.ca)
2004-04-06