# Quantum Electrodynamics

## 1st Edition

**Authors:**Iwo Białynicki-Birula Zofia Białynicka-Birula

**Editor:**D. Ter Haar

**eBook ISBN:**9781483280578

**Imprint:**Pergamon

**Published Date:**1st January 1975

**Page Count:**566

## Description

Quantum Electrodynamics focuses on the formulation of quantum electrodynamics (QED) in its most general and most abstract form: relativistic quantum field theory. It describes QED as a program, rather than a closed theory, that rests on the theory of the quantum Maxwellian field interacting with given (external) classical sources of radiation and on the relativistic quantum mechanics of electrons interacting with a given (external) classical electromagnetic field.

Comprised of eight chapters, this volume begins with an introduction to the fundamental principles of quantum theory formulated in a general, abstract fashion. The following chapters consider non-relativistic quantum mechanics; the theory of the electromagnetic field interacting with given sources of radiation; the quantum mechanics of particles; and the relativistic quantum mechanics of mutually non-interacting electrons moving in a given electromagnetic field. The formulation of QED is then described, paying particular attention to perturbation theory and Feynman diagrams and electron-photon processes. The final two chapters deal with renormalization theory and applications of QED.

This book is addressed to readers who are familiar with quantum mechanics and classical electrodynamics at the level of university courses.

## Table of Contents

Preface

Introduction

Chapter 1: The General Principles of Quantum Theory

1. The Postulates of Quantum Theory

The Time Evolution of a System

Causality

2. Symmetries

3. Canonical Quantization

Chapter 2: Non-Relativistic Quantum Mechanics

4. The Quantum Mechanics of a Particle

The Particle Propagator

The Scattering Amplitude

The S Matrix

5. The Many-Particle System

Spin and Statistics

Scattering in an External Potential

The Occupation-Number Representation

Creation and Annihilation Operators

Field Operators

Scattering and the S Operator

The Theory of Propagators and Feynman Diagrams

Chapter 3: The Classical Theory of the Electromagnetic Field

6. The Tensor Description of the Electromagnetic Field and the Field Equations

The Field Equations

Transformation Laws

Energy-Momentum Tensor of Electromagnetic Field

The Conservation Laws

7. Canonical Formalism for the Electromagnetic Field

The Generalized Poisson Brackets

Canonical Transformations and Their Generators

Poincaré Transformations as Canonical Transformations

8. The Electromagnetic Field with Sources

Charged Fluid

Charged Particles

Magnetic Charges

Charged Field

9. The Maxwellian Field

Solution of the Initial-Value Problem and the Poisson Brackets

Fourier Analysis of the Field

Conformal Transformations

The Maxwellian Field with External Sources

The Radiation Field

Multipole Radiation

Radiation of a Point Particle

Chapter 4: The Quantum Theory of the Electromagnetic Field

10. Canonical Quantization of the Electromagnetic Field

The Poincaré Group as a Symmetry Group

11. Quantization of the Free Maxwellian Field

Relativistic Invariance

Photons

Coherent States

Coherence of Electromagnetic Radiation

12. The Interaction of the Quantum Electromagnetic Field with External Sources

13. The Formulation of the Quantum Theory of the Maxwellian Field with the Aid of Potentials

The Classical Theory

The Quantum Theory of the Free Field

The Quantum Theory of the Electromagnetic Field with External Sources

The Poincaré Group as the Symmetry Group of Amplitudes

A Simple Representation of Transition Amplitudes

Induced Processes in Intense Photon Beams

Many-Photon Propagators

14. The Proca Theory

The Classical Theory of a Vector Field with Mass

The Quantum Theory of a Vector Field with Mass

The S Operator in the Presence of External Sources

15. The Infrared Catastrophe

Chapter 5: Relativistic Quantum Mechanics of Electrons

16. The Dirac Equation and the Symmetries of Its Solutions

The Properties of Solutions of the Dirac Equation without Potential

17. Electron Scattering in the Electromagnetic Field

Electron Wave Functions

The Green's Functions for the Dirac Equation

The Electron in a Static Electromagnetic Field

The Properties of the S Matrix for an Electron in an External Field

The Indistinguishability of Particles and the Vacuum-to-Vacuum Transition Amplitude

18. Electron Field Operators

Creation and Annihilation Operators

Field Operators

Electrons in an External Electromagnetic Field

The S Operator

Propagators

Chapter 6: The Formulation of Quantum Electrodynamics

19. The General Postulates of Quantum Electrodynamics

The Fundamental Dynamical Postulate

20. Perturbation Theory and Feynman Diagrams

The General Principles of Constructing Feynman Diagrams

Analysis of the Connectedness of Propagators

21. Photon Processes

The Relation between Transition Amplitudes and Propagators

The Källén—Lehmann Representation of the photon Propagator

Renormalization of an External Current

22. Electron-Photon Processes

Compensating Current

Electron-Photon Propagators

The Relation between the Compensating Current and the Gauge

Feynman Diagrams

The Relation between Propagators and Transition Amplitudes

Feynman Diagrams in Momentum Representation

Chapter 7: Renormalization Theory

23. The Necessity for Renormalization

The Electron Propagator

The Photon Propagator

The Vertex Function

Charge Renormalization

24. Equations for Renormalized Propagators

Set of Equations for Propagators

Elimination of the Field Aμ(z)

Gauge Invariance and the Ward Identity

Symmetric Expressions for the Electron and Photon Propagators and the Vertex Function

The Skeleton Structure of Diagrams

Renormalization

25. Renormalized Perturbation Theory

The General Properties of Renormalized Perturbation Theory

Renormalized Transition Probabilities

Independence of Transition Probabilities from the Compensating Current

The Infrared Catastrophe

Chapter 8: Applications of Quantum Electrodynamics

26. Two-Particle Collisions

The General Formulae for Two-Particle Processes

Negaton-Negaton Scattering

Photon-Negaton Scattering

Photon-Photon Scattering

27. Non-linear Effects in Quantum Electrodynamics

28. The Electron in a Static Electromagnetic Field

The Effective Field and the Polarization of the Vacuum

The Motion of the Electron in a Static Field

The Magnetic Moment of the Electron

The Lamb-Retherford Shift

29. The Limits of Applicability of Quantum Electrodynamics

Concluding Remarks

Appendices

Appendix A: Hilbert Space

Linear Operators

Appendix B: Chronological and Normal Products

The Chronological Product

The Normal Product

Appendix C: Functional Differentiation

Appendix D: The Poincaré Group

Appendix E: Green's Functions

The Schrödinger Equation

The Klein—Gordon and d'Alembert Equations

The Dirac and Proca Equations

Appendix F: The Symmetrie Energy-Momentum Tensor

Appendix G: Evaluation of Some Poisson Brackets

Appendix H: Some Operator Identities

Appendix I: Spinors

Appendix J: The Properties of Solutions of the Dirac Equations

Appendix K: Regularization

Appendix L: Methods of Calculating Integrals over Momentum Space

Appendix M: Representation of the S Matrix as a Double Limit of the Propagator

References

Articles

Textbooks and Monographs

Index of Symbols

Subject Index

Other Titles in the Series in Natural Philosophy

## Details

- No. of pages:
- 566

- Language:
- English

- Copyright:
- © Pergamon 1975

- Published:
- 1st January 1975

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483280578