The Classical Theory of Fields, Volume 2

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Butterworth-Heinemann, 1975 - Science - 402 pages
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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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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
 

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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
INDEX
425
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About the author (1975)

Lev Davidovich Landau was born on January 22, 1908 in Baku, U.S.S.R (now Azerbaijan). A brilliant student, he had finished secondary school by the age of 13. He enrolled in the University of Baku a year later, in 1922, and later transferred to the University of Leningrad, from which he graduated with a degree in physics. Landau did graduate work in physics at Leningrad's Physiotechnical Institute, at Cambridge University in England, and at the Institute of Theoretical Physics in Denmark, where he met physicist Neils Bohr, whose work he greatly admired. Landau worked in the Soviet Union's nuclear weapons program during World War II, and then began a teaching career. Considered to be the founder of a whole school of Soviet theoretical physicists, Landau was honored with numerous awards, including the Lenin Prize, the Max Planck Medal, the Fritz London Prize, and, most notably, the 1962 Nobel Prize for Physics, which honored his pioneering work in the field of low-temperature physics and condensed matter, particularly liquid helium. Unfortunately, Landau's wife and son had to accept the Nobel Prize for him; Landau had been seriously injured in a car crash several months earlier and never completely recovered. He was unable to work again, and spent the remainder of his years, until his death in 1968, battling health problems resulting from the accident. Landau's most notable written work is his Course of Theoretical Physics, an eight-volume set of texts covering the complete range of theoretical physics. Like several other of Landau's books, it was written with Evgeny Lifshitz, a favorite student, because Landau himself strongly disliked writing. Some other works include What is Relativity?, Theory of Elasticity, and Physics for Everyone.

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