The Classical Theory of FieldsLev Davidovich Landau, Lev Davydovič Landau (Physicien, Union Soviétique), Евгений Михайлович Лифшиц The 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. |
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waste
Although the above course is comprehensive, it is anything but easy. The intractability stems from the often very succinct derivation of expressions that require very advanced mathematical background to obtain. In rare cases there are some red flags in the text, like ... after a long calculation, we obtain ... . As often as not, however, the whoppers come out of the blue and stop the poor student in his tracks wondering whether his long night hours over the math textbook have been worth it. Not surprisingly, the only thing that can be born in the head of the desperate student in such a moment, is an anecdote. Here is one, exactly to the point:
Landau and Lifschitz are writing their ... let's say 137th physics textbook. Trying to prove some complex theorem, they've been sweating the proof all of the past week. Monday morning in runs Lifschitz, his clothes mismatched, his face red, his hands shaking...
Landau: My, you look horrible. What's going on?..
Lifschitz:Well, last night I (finally!) finished the proof, put all of the pages into a folder, and ... and I lost it in the subway! On my way here!..
Landau: Hmm ... I guess we'll have to do the same as last time – we'll just write "obviously, it follows that ... "
I think that the problems for the readers/students come from the mathematical genius of Landau. Mentally making all the intermediate calculations, he expects from his readers to follow him easily with the help of pen and paper. Very few of us justify these expectations.
For some notes that expand the intermediate calculations, see:
http://lantonov.tripod.com/index.html
Contents
THE PRINCIPLE OF RELATIVITY | 1 |
2 Intervals | 3 |
3 Proper time | 7 |
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 | |