Foundations of classical and quantum electrodynamics:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2014
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIX, 713 S. graph. Darst. |
| ISBN: | 9783527411535 |
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| adam_text |
Titel: Foundations of classical and quantum electrodynamics
Autor: Toptygin, I. N
Jahr: 2014
Contents
Preface XI
Fundamental Constants and Frequently Used Numbers XV
Basic Notation XVII
1 The Mathematical Methods of Electrodynamics 1
1.1 Vector and Tensor Algebra 1
1.1.1 The Definition of a Tensor and Tensor Operations 1
1.1.2 The Principal Values and Invariants ofa Symmetrie Tensor of Rank 2 8
1.1.3 Covariant and Contravariant Components 11
1.1.4 Tensors in Curvilinear and Nonorthogonal Systems of Coordinates 14
1.2 Vector and Tensor Calculus 18
1.2.1 Gradient and Directional Derivative. Vector Lines 19
1.2.2 Divergence and Curl. Integral Theorems 23
1.2.3 Solenoidal and Potential (Curl-less) Vectors 27
1.2.4 Differential Operations of Second Order 27
1.2.5 Differentiating in Curvilinear Coordinates 31
1.2.6 Orthogonal Curvilinear Coordinates 35
1.3 The Special Functions of Mathematical Physics 41
1.3.1 Cylindrical Functions 41
1.3.2 Spherical Functions and Legendre Polynomials 49
1.3.3 Dirac Delta Function 56
1.3.4 Certain Representations ofthe Delta Function 59
1.3.5 The Representation ofthe Delta Function through Loop Integrals in a
Complex Plane 60
1.3.6 Expansion in Total Systems of Orthogonal and Normalized Functions.
General Considerations 63
1.3.7 Fourier Series 66
1.3.8 Fourier Integral 68
1.4 Answers and Solutions 71
2 Basic Concepts of Electrodynamics: The Maxwell Equations 91
2.1 Electrostatics 91
2.1.1 The Coulomb Law 91
VI | Contents
2.1.2 Electric Field 92
2.1.3 Energy and Forces in Electrostatic Fields 107
2.2 Magnetostatics 112
2.2.1 Current Density and the Magnetic Field. Biot-Savart Law 112
2.2.2 Lorentz Force and Ampere's Formula 114
2.2.3 Conservation of Electric Charge and the Continuity Equation 114
2.2.4 Equations of Magnetostatics. Vector Potential 116
2.2.5 Energy and Forces in Magnetostatic Fields 124
2.3 Maxwell's Equations. Free Electromagnetic Field 131
2.3.1 The Law of Electromagnetic Induction 131
2.3.2 The Systems of Measurement Units of Electric and Magnetic
Values 135
2.3.3 An Analysis ofthe System of Maxwell's Equations 136
2.3.4 Free Electromagnetic Field 141
2.3.5 The Partial Polarization of Waves 144
2.3.6 Analytical Signal 149
2.3.7 The Hamiltonian Form of Equations for a Free Electromagnetic
Field 150
2.4 Answers and Solutions 154
3 The Special Theory of Relativity and Relativistic Kinematics 193
3.1 The Principle of Relativity and Lorentz Transformations 193
3.1.1 Properties of Space-Time and Intervals 193
3.1.2 Lorentz Transformations 198
3.1.3 Pseudo-Euclidean Geometry 202
3.2 Kinematics of Relativistic Particles 214
3.2.1 Energy and Momentum 214
3.2.2 Kinematic Problems 219
3.3 Answers and Solutions 233
4 Fundamentals of Relativistic Mechanics and Field Theory 271
4.1 Four-Dimensional Vectors and Tensors 271
4.1.1 Transformations of Tensors 271
4.1.2 Dual Tensors 276
4.2 The Motion of Charged Particles in Electromagnetic Fields.
Transformation ofthe Electric Field 280
4.2.1 Interaction of Charged Particles with the Electromagnetic Field 280
4.2.2 Equations of Motion of a Relativistic Particle 282
4.2.3 Transformations of Electromagnetic Field Stress 288
4.2.4 Dynamics of Orbital and Spin Magnetic Moments 298
4.2.5 The Approximate Methods. Averaging over Rapid Movements 301
4.3 The Four-Dimensional Formulation of Electrodynamics.
Introduction to Field Theory 313
4.3.1 Lagrangian and Hamiltonian Methods in Field Theory 313
4.3.2 The Action for an Electromagnetic Field 319
4.3.3 Noether's Theorem and Integrals of Motion 322
Contents Vll
4.4 Answers and Solutions 332
5 Emission and Scatteringof Electromagnetic Waves 395
5.1 Green's Functions and Retarded Potentials 395
5.1.1 The Green's Function ofa Wave Equation 396
5.1.2 Retarded Potentials 398
5.1.3 The Spectral Composition of Emission 400
5.2 Emission in Nonrelativistic Systems of Charges and Currents 404
5.2.1 Electric Dipole Emission 405
5.2.2 Quadrupole and Magnetic Dipole Emission 406
5.2.3 The Hertz Vector and Antenna Radiation 408
5.3 Emission by Relativistic Particles 416
5.3.1 The Electromagnetic Field ofa Propagating Charged Particle 416
5.3.2 The Loss of Energy and Momentum ofa Charged Particle 420
5.3.3 The Spectral Distribution of Radiation Emitted by Relativistic
Particles 423
5.3.4 Radiation from Colliding Particles 425
5.3.5 Radiation from Particle Decays and Transformations 427
5.4 Interaction of Charged Particles with Radiation 436
5.4.1 Interaction of a Charged Particle with its Own Electromagnetic
Field 436
5.4.2 Renormalization of Mass. The Radiation Damping Force in the
Relativistic Case 438
5 A3 Scattering of Electromagnetic Waves by Particles 443
5.5 Answers and Solutions 449
6 Quantum Theory of Radiation Processes. Photon Emission and
Scattering 513
6.1 Quantum Theory ofthe Free Electromagnetic Field 513
6.1.1 Field Oscillators 513
6.1.2 Photons 514
6.1.3 Occupation Number Representation and Operators of the
Electromagnetic Field 516
6.1.4 Coherent States 523
6.1.5 Representation ofthe Quantum States and the Operators in the Basis
of Coherent States 526
6.1.6 Squeezed States 529
6.1.7 Entangled States 533
6.1.8 Beamsplitters 535
6.2 Quantum Theory of Photon Emission, Absorption, and Scattering
by Atomic Systems 539
6.2.1 Interaction ofthe Quantized Electromagnetic Field with a Nonrelativistic
System 540
6.2.2 Spontaneous and Stimulated Emission 541
6.2.3 Electric Dipole Radiation 545
6.2.4 Electric Quadrupole and Magnetic Dipole Radiation 546
Vlll I Contents
6.2.5 Perturbation Theory for the Density Matrix 549
6.2.6 Long-Wavelengfh Dipole Approximation 552
6.3 Interaction between Relativistic Particles 560
6.3.1 The Relativistic Dirac Equation for Fermions 560
6.3.2 The Klein-Gordon-Fock Equation 563
6.3.3 The Analysis ofthe Dirac Equation 564
6.3.4 The Interaction Operator ofa Relativistic Particle with Photons 573
6.3.5 Method of Equivalent Photons 577
6.4 Answers and Solutions 581
7 Fundamentals of Quantum Theory ofthe Electron-Positron Field 631
7.1 Covariant Form of the Dirac Equation. Relativistic Bispinor
Transformation 631
7.2 Covariant Quadratic Forms 636
7.3 Charge Conjugation and Wave Functions of Antiparticles 639
7.4 Secondary Quantization ofthe Dirac Field. Creation and Annihilation
Operators for Field Quanta 640
7.5 Energy and Current Density Operators for Dirac Particles 643
7.6 Interaction between Electron-Positron and Electromagnetic Fields 645
7.7 Schrödinger Equation for Interacting Fields and the Evolution
Operator 647
7.8 Scattering Matrix and Its Calculation 649
7.9 Calculations of Probabilities and Effective Differential Cross-
Sections 652
7.10 Scattering ofa Relativistic Particle with a Spin in the Coulomb Field 653
7.11 Green's Functions of Electron-Positron and Electromagnetic Fields 657
7 AI Interaction between Electrons and Muons 662
7.IIA Electron-Muon Collisions 662
7.12.2 Conversionof an Electron-Positron Pair into a Muon Pair 666
7.13 Higher-Order Corrections 667
7.14 Answers and Solutions 669
Appendix A Conversion of Electric and Magnetic Quantities between the
International System of Units and the Gaussian System 675
Appendix B Variation Principle for Continuous Systems 677
B.l Vibrations of an Elastic Medium as the Vibration Limit of Discrete Point
Masses 677
B.2 The Lagrangian Form of Equations of Motion for a Continuous
Medium 680
Appendix C General Outline of Quantum Theory 685
C.l Spectrum ofPhysical Values and the Wave Function 685
C.2 State Vector 686
C.3 Indistinguishabilityof Identical Particles 687
CA Operators and Their Properties 688
C.5 Some Useful Formulas of Operator Algebra 698
Contents I IX
C.6 Wave Functions ofthe Hydrogen-Like Atom (the Lowest Levels) 699
C.6.1 Addition ofAngular Moments 700
C.6.2 Spin Operators and Wave Functions of Fermions (s = 1/2) 700
References 703
Index 709 |
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| spelling | Toptygin, I. N. 1931- Verfasser (DE-588)1054879826 aut Foundations of classical and quantum electrodynamics Igor N. Toptygin Weinheim Wiley-VCH 2014 XIX, 713 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantenelektrodynamik (DE-588)4047982-1 gnd rswk-swf Elektrodynamik (DE-588)4014251-6 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Elektrodynamik (DE-588)4014251-6 s DE-604 Quantenelektrodynamik (DE-588)4047982-1 s Erscheint auch als Online-Ausgabe, EPUB 978-3-527-67751-1 Erscheint auch als Online-Ausgabe, MOBI 978-3-527-67748-1 Erscheint auch als Online-Ausgabe, PDF 978-3-527-67749-8 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4329636&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026119797&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Toptygin, I. N. 1931- Foundations of classical and quantum electrodynamics Quantenelektrodynamik (DE-588)4047982-1 gnd Elektrodynamik (DE-588)4014251-6 gnd |
| subject_GND | (DE-588)4047982-1 (DE-588)4014251-6 (DE-588)4123623-3 |
| title | Foundations of classical and quantum electrodynamics |
| title_auth | Foundations of classical and quantum electrodynamics |
| title_exact_search | Foundations of classical and quantum electrodynamics |
| title_full | Foundations of classical and quantum electrodynamics Igor N. Toptygin |
| title_fullStr | Foundations of classical and quantum electrodynamics Igor N. Toptygin |
| title_full_unstemmed | Foundations of classical and quantum electrodynamics Igor N. Toptygin |
| title_short | Foundations of classical and quantum electrodynamics |
| title_sort | foundations of classical and quantum electrodynamics |
| topic | Quantenelektrodynamik (DE-588)4047982-1 gnd Elektrodynamik (DE-588)4014251-6 gnd |
| topic_facet | Quantenelektrodynamik Elektrodynamik Lehrbuch |
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