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Quantum Electrodynamics
- 1st Edition - January 1, 1975
- Authors: Iwo Białynicki-Birula, Zofia Białynicka-Birula
- Editor: D. Ter Haar
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 3 7 8 - 9
- Hardback ISBN:9 7 8 - 0 - 0 8 - 0 1 7 1 8 8 - 3
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 8 0 5 7 - 8
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… Read more
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Request a sales quoteQuantum 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.
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
- No. of pages: 566
- Language: English
- Edition: 1
- Published: January 1, 1975
- Imprint: Pergamon
- Paperback ISBN: 9781483233789
- Hardback ISBN: 9780080171883
- eBook ISBN: 9781483280578
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