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 ButterworthHeinemann. It comprises nine volumes, covering all branches of the subject; translations from the Russian are by leading scientists. 
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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  