Quantum Electrodynamics

Eugene Stefanovich

• Publisher: De Gruyter
• Year: 2018
• eBook ISBN: 9783110491432
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

This second volume of three on relativistic quantum theories of interacting charged particles discusses quantum theories of systems with variable numbers of particles. Basics of the Fock space and quantum electrodynamics are covered with an emphasis on renormalization. In contrast to the usual treatment of the topic, particles (rather than fields) are chosen as basic ingredients.

Contents
Fock space
Scattering in Fock space
Quantum electrodynamics
Renormalization
Useful integrals
Quantum fields of fermions
Quantum field of photons
QED interaction in terms of particle operators
Relativistic invariance of QFT
Loop integrals in QED
Scattering matrix in ( v / c ) 2 approximation
Checks of physical dimensions

1Fock space

There are more things in Heaven and on earth, dear Horacio, than are dreamed of in your
philosophy.
Hamlet

In this chapter, we construct the Fock space ℋ populated by particles of five types: electrons e−, positrons e+, protons p+, antiprotons2 p− and photons γ. We will practice constructions of simple interaction operators and study their properties. In comparison with Volume 1, the main novelty is in working with operators that change the number of particles. This will prepare us for mastering a more realistic theory – quantum electrodynamics (QED) – in Chapters 3 and 4.

1.1Creation and annihilation operators

Here we introduce the concepts of creation and annihilation operators. Though lacking autonomous physical meaning, these operators greatly simplify cal...

Table of contents

• Cover
• Title Page
• Copyright
• Contents
• List of figures
• List of tables
• Postulates, statements, theorems
• Conventional notation
• Preface
• 1 Fock space
• 2 Scattering in Fock space
• 3 Quantum electrodynamics
• 4 Renormalization
• A Useful integrals
• B Quantum fields of fermions
• C Quantum field of photons
• D QED interaction in terms of particle operators
• E Relativistic invariance of QFT
• F Loop integrals in QED
• G Scattering matrix in (v/c)2 approximation
• H Checks of physical dimensions
• Bibliography
• Index