Gingrich Practical Quantum Electrodynamics

Erscheinungsjahr 2006
ISBN: 978-1-4200-1068-8
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 360 Seiten

Reihe: Pure and Applied Physics

Taking a heuristic approach to relativistic quantum mechanics, Practical Quantum Electrodynamics provides a complete introduction to the theory, methodologies, and calculations used for explaining the physical interaction of charged particles.

This book combines the principles of relativity and quantum theory necessary for performing the calculations of the electromagnetic scattering of electrons and positrons and the emission and absorption of photons. Beginning with an introduction of the wave equations for spin-0 and spin-1/2 particles, the author compares and contrasts the relativistic and spin effects for both types of particles. He emphasizes how the relativistic treatment of quantum mechanics and the spin-1/2 degree of freedom are necessary to describe electromagnetic interactions involving electron scattering and points out the shortfalls of the wave-equation approach to relativistic quantum mechanics. Developing the Feynman rules for quantum electrodynamics by example, the book offers an intuitive, hands-on approach for performing fundamental calculations. It also illustrates how to perform calculations that can be related to experiments such as diagrams, lifetimes, and cross sections.

Practical Quantum Electrodynamics builds a strong foundation for further studies and research in theoretical and particle physics, particularly relativistic quantum field theory or nonrelativistic many-body theory.

Zielgruppe

Students studying advanced or relativistic quantum mechanics, graduate students and researchers in particle physics, field theory, and astrophysics.

Autoren/Hrsg.

Gingrich, Douglas M.

Fachgebiete

• Naturwissenschaften Physik Quantenphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Part I: INTRODUCTION AND BACKGROUND
Introduction
Problems
Notation and Conventions
Units
Maxwell's Equations in Vacuum
Coordinates
Metric Tensor
Covariant and Contravariant Indices
Three-Vector, Four-Vector, and Scalar Product
Classification of Four-Vectors
Gradient and Differential Operators
Pauli Matrices
Groups
Useful Definitions
Problems
Lorentz Covariance
Lorentz Group
Lorentz Boost
Lorentz Covariance and Conservation Laws
Problems

Part II: RELATIVISTIC QUANTUM MECHANICS
Klein-Gordon Equation
Wave Equation for a Spin-0 Particle
Lorentz Covariance of the Klein-Gordon Equation
Plane-Wave Solutions of the Klein-Gordon Equation
General Solution of the Klein-Gordon Equation
Conserved Charge and Current
Normalization and Orthogonality
Interaction with the Electromagnetic Field
Hamiltonian Form of the Klein-Gordon Equation
Free-Particle Solutions and Wave Packets
Klein Paradox for Spin-0 Particles
Coulomb Interaction
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
Covariance of the Continuity Equation
Adjoint Spinor
Bilinear Covariants
Plane-Wave Solutions
Projection Operators for Energy and Spin
Hole Theory
Charge Conjugation
Time Reversal
Combined CPT Symmetry
Free-Particle Solutions and Wave Packets
Klein Paradox for Spin-1/2 Particles
Summary
Problems

Part III: QUANTUM ELECTRODYNAMICS
Propagator Methods
Nonrelativistic Scattering Theory
Green Functions and Integral Equations
The Born Approximation
Propagator Theory
The Nonrelativistic Propagator
Propagator in Relativistic Theory
Propagator for the Klein-Gordon Equation
Propagator for the Dirac Equation
S-Matrix
Problems
Photons
Maxwell's Equations
Gauge Transformations
Polarization Vectors
Photon Propagator
Problems
Quantum Electrodynamic Processes
Lifetimes and Cross Sections
Coulomb Scattering of Electrons
Trace Theorems
Coulomb Scattering of Positrons
Crossing Symmetry and Substitution Rules
Electron Scattering from a Dirac Proton
Bremsstrahlung
Photon-Electron Scattering
Electron-Positron Annihilation into Two Photons
Electron-Positron Pair Production
Electron-Electron Scattering
Electron-Positron Scattering
Beyond Tree Diagrams
Problems

Part IV: APPENDICES
A: Lorentz-Invariant Flux Factor
B: Lorentz-Invariant Phase Space
C: Feynman Rules for Tree Diagrams
D: Trace Calculation Using FORM

References
Index