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

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