Quantum Electrodynamics (eBook)

Front Cover 1
Quantum Electrodynamics 4
Copyright Page 5
Table of Contents 6
Preface 12
Introduction 18
Chapter 1: THE GENERAL PRINCIPLES OF QUANTUM THEORY 22
1. The Postulates of Quantum Theory 22
2. Symmetries 36
3. Canonical Quantization 40
Chapter 2: NON-RELATIVISTIC QUANTUM MECHANICS 43
4. The Quantum Mechanics of a Particle 43
5. The Many-Particle System 55
Chapter 3: THE CLASSICAL THEORY OF THE ELECTROMAGNETIC FIELD 104
6. The Tensor Description of the Electromagnetic Field and the Field Equations 104
7. Canonical Formalism for the Electromagnetic Field 112
8. The Electromagnetic Field with Sources 123
9. The Maxwelhan Field 140
Chapter 4: THE QUANTUM THEORY OF THE ELECTROMAGNETIC FIELD 173
10. Canonical Quantization of the Electromagnetic Field 173
11. Quantization of the Free Maxwellian Field 178
12. The Interaction of the Quantum Electromagnetic Field with External Sources 203
13. The Formulation of the Quantum Theory of the Maxwellian Field with the Aid of Potentials 212
14. The Proca Theory 232
15. The Infrared Catastrophe 241
Chapter 5: RELATIVISTIC QUANTUM MECHANICS OF ELECTRONS 247
16. The Dirac Equation and the Symmetries of Its Solutions . . . . 247
17. Electron Scattering in the Electromagnetic Field . 264
18. Electron Field Operators 310
Chapter 6: THE FORMULATION OF QUANTUM ELECTRODYNAMICS 328
19. The General Postulates of Quantum Electrodynamics 328
20. Perturbation Theory and Feynman Diagrams 333
21. Photon Processes 356
22. Electron-Photon Processes 369
Chapter 7: RENORMALIZATION THEORY 399
23. The Necessity for Renormalization 399
24. Equations for Renormalized Propagators 419
25. Renormalized Perturbation Theory 443
Chapter 8: APPLICATIONS OF QUANTUM ELECTRODYNAMICS 456
26. Two-Particle Collisions 456
27. Non-linear Effects in Quantum Electrodynamics 469
28. The Electron in a Static Electromagnetic Field 472
29. The Limits of Applicability of Quantum Electrodynamics . . . 483
Concluding Remarks 487
Appendices 490
Appendix A: Hilbert Space 490
Appendix B: Chronological and Normal Products 494
Appendk C: Functional Differentiation 499
Appendix D : The Poincaré Group 502
Appendix E: Green's Functions 508
Appendix F: The Symmetrie Energy-Momentum Tensor 516
Appendix G: Evaluation of Some Poisson Brackets 519
Appendix H: Some Operator Identities 521
Appendix I: Spinors 525
Appendix J: The Properties of Solutions of the Dirac Equations 533
Appendix K: Regularization 536
Appendix L: Methods of Calculating Integrals over Momentum Space 539
Appendix M: Representation of the S Matrix as a Double Limit of the Propagator 542
REFERENCES 544
INDEX OF SYMBOLS 552
SUBJECT INDEX 558
OTHER TITLES IN THE SERIES IN NATURAL PHILOSOPHY 566