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E-raamat: Electromagnetic Processes

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This book provides an understanding of the theoretical foundations for the calculation of electromagnetic processes. Photon production processes are particularly important in astrophysics, since almost all of our knowledge of distant astronomical objects comes from the detection of radiation from these sources. Further, the conditions therein are extremely varied and a wide variety of naturally occurring electromagnetic phenomena can be described by limiting forms of the basic theory.

The first chapter reviews some basic principles that are the underpinnings for a general description of electromagnetic phenomena, such as special relativity and, especially, relativistic covariance. Classical and quantum electrodynamics (QED) are then formulated in the next two chapters, followed by applications to three basic processes (Coulomb scattering, Compton scattering, and bremsstrahlung). These processes are related to other phenomena, such as pair production, and the comparisons are discussed.

A unique feature of the book is its thorough discussion of the nonrelativistic limit of QED, which is simpler than the relativistic theory in its formulation and applications. The methods of the relativistic theory are introduced and applied through the use of notions of covariance, to provide a shorter path to the more general theory. The book will be useful for graduate students working in astrophysics and in certain areas of particle physics.

Arvustused

"A remarkable intellectual achievement Few books make such a valiant and successful effort to explain the physics of these processes. This book fills an important gap in the literature."Malcolm Longair, Cambridge University "An excellent, well-written, and well-organized discourse that has a worthy place in the literature. It will provide a valuable graduate teaching and reference work for physicists and astrophysicists for years to come."Matthew Baring, Rice University "Solid and rich in physics. A very useful book for anyone interested in the physics of astrophysics."David Spergel, Princeton University "This is a clearly written and comprehensive book on electromagnetic processes by one of the leading experts in this area. The book covers both classical and quantum processes and discusses the relativistic and nonrelativistic limits. Both graduate students and researchers interested in the underlying processes by which radiation is produced will find Gould's book to be both easily understandable and extremely useful."George Blumenthal, University of California, Santa Cruz "Electromagnetic Processes is a lucid exposition of the physics that is fundamental for much of modern physics. Since our entire observational understanding of the universe thus far relies on such processes, this book is a timely addition to the lexicon for astronomy and astrophysics, for which its clear exposition of Compton scattering in the relativistic limit, for example, provides a welcome addition to the literature. Gould has wisely chosen to use cgs units, which makes its applications and familiarity to the astrophysicist that much more direct. Gould writes in a clear and complete style, with interesting historical notes to complement and accent the derivations. This book fills the gap between Jackson and Rybicki and Lightman and will serve both reference and textbook needs."Jonathan E. Grindlay, Robert Treat Paine Professor of Astronomy, Harvard University "Electromagnetic Processes fills an important niche in the spectrum of advanced texts on radiation processes for graduate students and professional astrophysicists. Gould provides a clear connection between classical and quantum treatments of basic processes like Compton scattering and bremsstrahlung, in both the non-relativistic and relativistic regimes. Standard texts generally provide a sketchy overview of the QED corrections, while books on QED itself are often difficult to weed through for the needed formulae. I highly recommend this book for those seeking a more complete overview of the basic physics of the interaction of radiation with charged particles."Steven M. Kahn, Stanford University "Electromagnetic Processes succeeds brilliantly in providing a unified treatment of the foundations of classical and quantum electrodynamics with clarity and scholarship and highlighting the intellectual beauty of the subject. This is the book to which students and researchers will turn as they struggle to solve problems in the countless applications of electrodynamics."Roger Blandford, Stanford University

Muu info

A remarkable intellectual achievement Few books make such a valiant and successful effort to explain the physics of these processes. This book fills an important gap in the literature. -- Malcolm Longair, Cambridge University An excellent, well-written, and well-organized discourse that has a worthy place in the literature. It will provide a valuable graduate teaching and reference work for physicists and astrophysicists for years to come. -- Matthew Baring, Rice University Solid and rich in physics. A very useful book for anyone interested in the physics of astrophysics. -- David Spergel, Princeton University This is a clearly written and comprehensive book on electromagnetic processes by one of the leading experts in this area. The book covers both classical and quantum processes and discusses the relativistic and nonrelativistic limits. Both graduate students and researchers interested in the underlying processes by which radiation is produced will find Gould's book to be both easily understandable and extremely useful. -- George Blumenthal, University of California, Santa Cruz Electromagnetic Processes is a lucid exposition of the physics that is fundamental for much of modern physics. Since our entire observational understanding of the universe thus far relies on such processes, this book is a timely addition to the lexicon for astronomy and astrophysics, for which its clear exposition of Compton scattering in the relativistic limit, for example, provides a welcome addition to the literature. Gould has wisely chosen to use cgs units, which makes its applications and familiarity to the astrophysicist that much more direct. Gould writes in a clear and complete style, with interesting historical notes to complement and accent the derivations. This book fills the gap between Jackson and Rybicki and Lightman and will serve both reference and textbook needs. -- Jonathan E. Grindlay, Robert Treat Paine Professor of Astronomy, Harvard University Electromagnetic Processes fills an important niche in the spectrum of advanced texts on radiation processes for graduate students and professional astrophysicists. Gould provides a clear connection between classical and quantum treatments of basic processes like Compton scattering and bremsstrahlung, in both the non-relativistic and relativistic regimes. Standard texts generally provide a sketchy overview of the QED corrections, while books on QED itself are often difficult to weed through for the needed formulae. I highly recommend this book for those seeking a more complete overview of the basic physics of the interaction of radiation with charged particles. -- Steven M. Kahn, Stanford University Electromagnetic Processes succeeds brilliantly in providing a unified treatment of the foundations of classical and quantum electrodynamics with clarity and scholarship and highlighting the intellectual beauty of the subject. This is the book to which students and researchers will turn as they struggle to solve problems in the countless applications of electrodynamics. -- Roger Blandford, Stanford University
Preface ix
Some Fundamental Principles
1(36)
Units and Characteristic Lengths, Times, Energies, Etc.
1(4)
Relativistic Covariance and Relativistic Invariants
5(10)
Spacetime Transformation
5(3)
Other Four-Vectors and Tensors---Covariance
8(2)
Some Useful and Important Invariants
10(3)
Covariant Mechanics and Electrodynamics
13(2)
Kinematic Effects
15(3)
Threshold Energies in Non-Relativistic and Relativistic Processes
15(2)
Transformations of Angular Distributions
17(1)
Binary Collision Rates
18(3)
Phase-Space Factors
21(16)
Introduction
21(2)
Simple Examples
23(3)
General Theorems---Formulation
26(2)
General Formulas---Evaluation of Multiple Integrals
28(4)
One-Particle Distributions
32(2)
Invariant Phase Space
34(3)
Classical Electrodynamics
37(38)
Retarded Potentials
37(4)
Fields, Potentials, and Gauges
37(2)
Retarded Potentials in the Lorentz Gauge
39(2)
Multipole Expansion of the Radiation Field
41(5)
Vector Potential and Retardation Expansion
41(2)
Multipole Radiated Power
43(3)
Fourier Spectra
46(3)
Fields of a Charge in Relativistic Motion
49(5)
Lienard-Wiechert Potentials
49(2)
Charge in Uniform Motion
51(2)
Fields of an Accelerated Charge
53(1)
Radiation from a Relativistic Charge
54(3)
Radiation Reaction
57(4)
Non-Relativistic Limit
57(3)
Relativistic Theory: Lorentz-Dirac Equation
60(1)
Soft-Photon Emission
61(4)
Multipole Formulation
61(1)
Dipole Formula
62(1)
Emission from Relativistic Particles
63(2)
Weizsacker-Williams Method
65(5)
Fields of a Moving Charge
66(2)
Equivalent Photon Fluxes
68(2)
Absorption and Stimulated Emission
70(5)
Relation to Spontaneous Emission
71(1)
General Multiphoton Formula
72(1)
Stimulated Scattering
73(2)
Quantum Electrodynamics
75(60)
Brief Historical Sketch
76(2)
Relationship with Classical Electrodynamics
78(2)
Non-Relativistic Formulation
80(14)
Introductory Remarks
80(1)
Classical Interaction Hamiltonian
80(3)
Quantum-Mechanical Interaction Hamiltonian
83(1)
Perturbation Theory
84(4)
Processes, Vertices, and Diagrams
88(6)
Relativistic Theory
94(15)
Modifications of the Non-Covariant Formulation
94(3)
Photon Interactions with Charges without Spin
97(6)
Spin-1/2 Interactions
103(4)
Invariant Transition Rate
107(2)
Soft-Photon Emission
109(14)
Non-Relativistic Limit
109(4)
Emission from Spin Transitions
113(3)
Relativistic Particles without Spin
116(3)
Relativistic Spin-1/2 Particles
119(4)
Special Features of Electromagnetic Processes
123(12)
``Order'' of a Process
123(4)
Radiative Corrections and Renormalization
127(3)
Kinematic Invariants
130(2)
Crossing Symmetry
132(3)
Elastic Scattering of Charged Particles
135(42)
Classical Coulomb Scattering
135(7)
Small-Angle Scattering
135(3)
General Case
138(1)
Two-Body Problem---Relative Motion
139(2)
Validity of the Classical Limit
141(1)
Non-Relativistic Born Approximation and Exact Treatment
142(14)
Perturbation-Theory Formulation
142(3)
Sketch of Exact Theory
145(3)
Two-Body Problem
148(2)
Scattering of Identical Particles
150(4)
Validity of the Born Approximation
154(2)
Scattering of Relativistic Particles of Zero Spin
156(10)
Coulomb Scattering
156(2)
Scattering of Two Distinguishable Charges
158(4)
Two Identical Charges
162(1)
Scattering of Charged Antiparticles
163(3)
Scattering of Relativistic Spin-1/2 Particles
166(11)
Spin Sums, Projection Operators, and Trace Theorems
166(4)
Coulomb Scattering
170(1)
Møller and Bhabha Scattering
171(6)
Compton Scattering
177(34)
Classical Limit
177(5)
Kinematics of the Scattering
177(1)
Derivation of the Thomson Cross Section
178(3)
Validity of the Classical Limit
181(1)
Quantum-Mechanical Derivation: Non-Relativistic Limit
182(4)
Interactions and Diagrams
182(2)
Calculation of the Cross Section
184(2)
Scattering by a Magnetic Moment
186(2)
Relativistic Spin-0 Case
188(3)
Relativistic Spin-1/2 Problem: Klein-Nishina Formula
191(6)
Formulation
191(2)
Evaluation of the Cross Section
193(1)
Invariant Forms
194(1)
Limiting Forms and Comparisons
195(2)
Relationship to Pair Annihilation and Production
197(2)
Double Compton Scattering
199(12)
Non-Relativistic Case. Soft-Photon Limit
199(3)
Non-Relativistic Case. Arbitrary Energy
202(5)
Extreme Relativistic Limit
207(4)
Bremsstrahlung
211(58)
Classical Limit
211(6)
Soft-Photon Limit
211(3)
General Case: Definition of the Gaunt Factor
214(3)
Non-Relativistic Born Limit
217(11)
General Formulation for Single-Particle Bremsstrahlung
217(5)
Coulomb (and Screened-Coulomb) Bremsstrahlung
222(1)
Born Correction: Sommerfeld-Elwert Factor
223(3)
Electron-Positron Bremsstrahlung
226(2)
Electron-Electron Bremsstrahlung. Non-Relativistic
228(8)
Direct Born Amplitude
228(4)
Photon-Emission Probability (without Exchange)
232(2)
Cross Section (with Exchange)
234(2)
Intermediate Energies
236(4)
General Result. Gaunt Factor
236(3)
Soft-Photon Limit
239(1)
Relativistic Coulomb Bremsstrahlung
240(14)
Spin-0 Problem
241(3)
Spin-1/2: Bethe-Heitler Formula
244(4)
Relativistic Electron-Electron Bremsstrahlung
248(3)
Weizsacker-Williams Method
251(3)
Electron-Atom Bremsstrahlung
254(15)
Low Energies
254(2)
Born Limit---Non-Relativistic
256(1)
Intermediate Energies---Non-Relativistic
257(2)
Relativistic Energies---Formulation
259(5)
Relativistic Energies---Results and Discussion
264(5)
Index 269
Robert J. Gould is Research Professor of Physics at the University of California, San Diego. His research focuses on atomic, nuclear, and particle processes; statistical mechanics; and applications of astrophysics.