The Classical Theory of Fields: Volume 2The fourth edition contains seven new sections with chapters on General Relativity, Gravitational Waves and Relativistic Cosmology. The text has been thoroughly revised and additional problems inserted. The Complete course of Theoretical Physics by Landau and Lifshitz, recognized as two of the world's outstanding physicists, is published in full by Butterworth-Heinemann. It comprises nine volumes, covering all branches of the subject; translations from the Russian are by leading scientists. |
Contents
THE PRINCIPLE OF RELATIVITY | 8 |
2 Intervals | 8 |
3 Proper time | 8 |
4 The Lorentz transformation | 9 |
5 Transformation of velocities | 12 |
6 Fourvectors | 14 |
7 Fourdimensional velocity | 23 |
RELATIVISTIC MECHANICS | 25 |
THE FIELD OF MOVING CHARGES | 171 |
63 The LienardWiechert potentials | 173 |
64 Spectral resolution of the retarded potentials | 176 |
65 The Lagrangian to terms of second order | 179 |
RADIATION OF ELECTROMAGNETIC WAVES | 184 |
67 Dipole radiation | 187 |
68 Dipole radiation during collisions | 191 |
69 Radiation of low frequency in collisions | 193 |
9 Energy and momentum | 26 |
10 Transformation of distribution functions | 30 |
11 Decay of particles | 32 |
12 Invariant crosssection | 36 |
13 Elastic collisions of particles | 38 |
14 Angular momentum | 42 |
CHARGES IN ELECTROMAGNETIC FIELDS | 46 |
16 Fourpotential of a field | 47 |
17 Equations of motion of a charge in a field | 49 |
18 Gauge invariance | 52 |
19 Constant electromagnetic Held | 53 |
20 Motion in a constant uniform electric faId | 55 |
21 Motion in a constant uniform magnetic field | 56 |
22 Motion of a charge in constant uniform electric and magnetic fields | 59 |
23 The electromagnetic Held tensor | 64 |
24 Lorentz transformation of the field | 66 |
25 Invariants of the field | 67 |
THE ELECTROMAGNETIC FIELD EQUATIONS | 70 |
27 The action function of the electromagnetic field | 71 |
28 The fourdimensional current vector | 73 |
29 The equation of continuity | 76 |
30 The second pair of Maxwell equations | 78 |
31 Energy density and energy flux | 80 |
32 The energymomentum tensor | 82 |
33 Energymomentum tensor of the electromagnetic field | 86 |
34 The virial theorem | 90 |
35 The energymomentum tensor for macroscopic bodies | 92 |
CONSTANT ELECTROMAGNETIC FIELDS | 95 |
37 Electrostatic energy of charges | 96 |
38 The field of a uniformly moving charge | 98 |
39 Motion in the Coulomb field | 100 |
40 The dipole moment | 103 |
41 Multipole moments | 105 |
42 System of charges in an external field | 108 |
43 Constant magnetic field | 110 |
44 Magnetic moments | 111 |
45 Larmors theorem | 113 |
ELECTROMAGNETIC WAVES | 116 |
47 Plane waves | 118 |
48 Monochromatic plane waves | 123 |
49 Spectral resolution | 128 |
50 Partially polarized light | 129 |
51 The Fourier resolution of the electrostatic field | 134 |
52 Characteristic vibrations of the field | 135 |
THE PROPAGATION OF LIGHT | 140 |
54 Intensity | 143 |
55 The angular eikonal | 145 |
56 Narrow bundles of rays | 147 |
57 Image formation with broad bundles of rays | 153 |
58 The limits of geometrical optics | 154 |
59 Diffraction | 156 |
60 Fresnel diffraction | 162 |
61 Fraunhofer diffraction | 165 |
70 Radiation in the case of Coulomb interaction | 195 |
71 Quadrupole and magnetic dipole radiation | 203 |
72 The field of the radiation at near distances | 206 |
73 Radiation from a rapidly moving charge | 210 |
74 Synchrotron radiation magnetic bremsstrahlung | 215 |
75 Radiation damping | 222 |
76 Radiation damping in the relativistic case | 226 |
77 Spectral resolution of the radiation in the ultrarelativistic case | 230 |
78 Scattering by free charges | 233 |
79 Scattering of lowfrequency waves | 238 |
80 Scattering of highfrequency waves | 240 |
PARTICLE IN A GRAVITATIONAL FIELD | 243 |
82 The gravitational field in relativistic mechanics | 244 |
83 Curvilinear coordinates | 247 |
84 Distances and time intervals | 251 |
85 Covariant differentiation | 255 |
86 The relation of the Christoffel symbols to the metric tensor | 260 |
87 Motion of a particle in a gravitational field | 263 |
88 The constant gravitational field | 266 |
89 Rotation | 273 |
90 The equations of electrodynamics in the presence of a gravitational field | 275 |
THE GRAVITATIONAL FIELD EQUATIONS | 278 |
92 Properties of the curvature tensor | 281 |
93 The action function for the gravitational field | 287 |
94 The energymomentum tensor | 290 |
95 The Einstein equations | 295 |
96 The energymomentum pseudotensor of the gravitational field | 301 |
97 The synchronous reference system | 307 |
98 The tetrad representation of the Einstein equations | 313 |
THE FIELD OF GRAVITATING BODIES | 316 |
100 The centrally symmetric gravitational Held | 320 |
101 Motion in a centrally symmetric gravitational field | 328 |
102 Gravitational collapse of a spherical body | 331 |
103 Gravitational collapse of a dustlike sphere | 338 |
104 Gravitational collapse of nonspherical and rotating bodies | 344 |
105 Gravitational Holds at large distances from bodies | 353 |
106 The equations of motion of a system of bodies in the second approximation | 360 |
GRAVITATIONAL WAVES | 368 |
108 Gravitational waves in curved spacetime | 370 |
109 Strong gravitational waves | 373 |
110 Radiation of gravitational waves | 376 |
RELATIVISTIC COSMOLOGY | 382 |
112 The closed isotropic model | 386 |
113 The open isotropic model | 390 |
114 The red shift | 394 |
115 Gravitational stability of an isotropic universe | 400 |
116 Homogeneous spaces | 406 |
117 The flat anisotropic model | 412 |
118 Oscillating regime of approach to a singular point | 416 |
119 The time singularity in the general cosmological solution of the Einstein equations | 420 |
425 | |
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Common terms and phrases
angle angular momentum antisymmetric arbitrary average axis body calculate centre Christoffel symbols components condition consider const constant coordinate system corresponding covariant curvature tensor curvilinear coordinates denote density derivatives determined differentiation dipole direction distance ds² Einstein equations electric field electromagnetic field element energy energy-momentum tensor equal equations of motion expressed in terms formula four-dimensional four-momentum four-vector four-velocity frequency function galilean geometrical optics given gravitational field hypersurface infinity integral intensity interval invariant Lagrangian magnetic field mass metric tensor obtain optical particle Paß perpendicular polarization problem propagation quantities radiation radius vector rays reference frame reference system relation relativistic rotation scalar sin² solution space space-time Substituting system of reference three-dimensional transformation values vanish vector potential velocity of light wave vector world line write zero Απ