EXCERPTS FROM THE PREFACES TO THE FIRST AND SECOND EDITIONS PREFACE TO THE FOURTH ENGISH EDITION EDITOR'S PREFACE TO THE SEVENTH RUSSIAN EDITION NOTATION CHAPTER 1. THE PRINCIPLE OF RELATIVITY 1 Velocity of propagation of interaction 2 Intervals 3 Proper time 4 The Lorentz transformation 5 Transformation of velocities 6 Four-vectors 7 Four-dimensional velocity CHAPTER 2. RELATIVISTIC MECHANICS 8 The principle of least action 9 Energy and momentum 10 Transformation of distribution functions 11 Decay of particles 12 Invariant cross-section 13 Elastic collisions of particles 14 Angular momentum CHAPTER 3. CHARGES IN ELECTROMAGNETIC FIELDS 15 Elementary particles in the theory of relativity 16 Four-potential of a field 17 Equations of motion of a charge in a field 18 Gauge invariance 19 Constant electromagnetic field 20 Motion in a constant uniform electric field 21 Motion in a constant uniform magnetic field 22 Motion of a charge in constant uniform electric and magnetic fields 23 The electromagnetic field tensor 24 Lorentz transformation of the field 25 Invariants of the field CHAPTER 4. THE ELECTROMAGNETIC FIELD EQUATIONS 26 The first pair of Maxwell's equations 27 The action function of the electromagnetic field 28 The four-dimensional current vector 29 The equation of continuity 30 The second pair of Maxwell equations 31 Energy density and energy flux 32 The energy-momentum tensor 33 Energy-momentum tensor of the electromagnetic field 34 The virial theorem 35 The energy-momentum tensor for macroscopic bodies CHAPTER 5. CONSTANT ELECTROMAGNETIC FIELDS 36 Coulomb's law 37 Electrostatic energy of charges 38 The field of a uniformly moving charge 39 Motion in the Coulomb field 40 The dipole moment 41 Multipole moments
42 System of charges in an external field 43 Constant magnetic field 44 Magnetic moments 45 Larmor's theorem CHAPTER 6. ELECTROMAGNETIC WAVES 46 The wave equation 47 Plane waves 48 Monochromatic plane waves 49 Spectral resolution 50 Partially polarized light 51 The Fourier resolution of the electrostatic field 52 Characteristic vibrations of the field CHAPTER 7. THE PROPAGATION OF LIGHT 53 Geometrical optics54 Intensity 55 The angular eikonal 56 Narrow bundles of rays 57 Image formation with broad bundles of rays 58 The limits of geometrical optics 59 Diffraction 60 Fresnel diffraction 61 Fraunhofer diffraction CHAPTER 8. THE FIELD OF MOVING CHARGES 62 The retarded potentials 63 The Lienard-Wiechert potentials 64 Spectral resolution of the retarded potentials 65 The Lagrangian to terms of second order CHAPTER 9. RADIATION OF ELECTROMAGNETIC WAVES 66 The field of a system of charges at large distances 67 Dipole radiation 68 Dipole radiation during collisions 69 Radiation of low frequency in collisions 70 Radiation in the case of Coulomb interaction 71 Quadrupole and magnetic dipole radiation 72 The field of the radiation at near distances 73 Radiation from a rapidly moving charge 74 Synchrotron radiation (magnetic bremsstrahlung) 75 Radiation damping 76 Radiation damping in the relativistic case 77 Spectral resolution of the radiation in the ultrarelativistic case 78 Scattering by free charges 79 Scattering of low-frequency waves 80 Scattering of high-frequency waves CHAPTER 10. PARTICLE IN A GRAVITATIONAL FIELD 81 Gravitational fields in nonrelativistic mechanics 82 The gravitational field in relativistic mechanics 83 Curvilinear coordinates 84 Distances and time intervals 85 Covariant differentiation 86 The relation of the Christoffel symbols to the metric tensor 87 Motion of a particle in a gravitational field
88 The constant gravitational field 89 Rotation 90 The equations of electrodynamics in the presence of a gravitational field CHAPTER 11. THE GRAVITATIONAL FIELD EQUATIONS 91 The curvature tensor 92 Properties of the curvature tensor 93 The action function for the gravitational field 94 The energy-momentum tensor 95 The Einstein equations 96 The energy-momentum pseudotensor of the gravitational field 97 The synchronous reference system 98 The tetrad representation of the Einstein equations CHAPTER 12. THE FIELD OF GRAVITATING BODIES 99 Newton's law 100 The centrally symmetric gravitational field 101 Motion in a centrally symmetric gravitational field 102 Gravitational collapse of a spherical body 103 Gravitational collapse of a dustlike sphere 104 Gravitational collapse of nonspherical and rotating bodies 105 Gravitational fields at large distances from bodies 106 The equations of motion of a system of bodies in the second approximation CHAPTER 13. GRAVITATIONAL WAVES 107 Weak gravitational waves 108 Gravitational waves in curved space-time 109 Strong gravitational waves 110 Radiation of gravitational waves CHAPTER 14. RELATIVISTIC COSMOLOGY 111 Isotropic space 112 The closed isotropic model 113 The open isotropic model 114 The red shift 115 Gravitational stability of an isotropic universe 116 Homogeneous spaces 117 The flat anisotropic model 118 Oscillating regime of approach to a singular point 119 The time singularity in the general cosmological solution of the Einstein equations INDEX
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