Applications of the Theory of Groups in Mechanics and Physics

Couverture
Springer Science & Business Media, 30 avr. 2004 - 446 pages
The notion of group is fundamental in our days, not only in mathematics, but also in classical mechanics, electromagnetism, theory of relativity, quantum mechanics, theory of elementary particles, etc. This notion has developed during a century and this development is connected with the names of great mathematicians as E. Galois, A. L. Cauchy, C. F. Gauss, W. R. Hamilton, C. Jordan, S. Lie, E. Cartan, H. Weyl, E. Wigner, and of many others. In mathematics, as in other sciences, the simple and fertile ideas make their way with difficulty and slowly; however, this long history would have been of a minor interest, had the notion of group remained connected only with rather restricted domains of mathematics, those in which it occurred at the beginning. But at present, groups have invaded almost all mathematical disciplines, mechanics, the largest part of physics, of chemistry, etc. We may say, without exaggeration, that this is the most important idea that occurred in mathematics since the invention of infinitesimal calculus; indeed, the notion of group expresses, in a precise and operational form, the vague and universal ideas of regularity and symmetry. The notion of group led to a profound understanding of the character of the laws which govern natural phenomena, permitting to formulate new laws, correcting certain inadequate formulations and providing unitary and non contradictory formulations for the investigated phenomena.
 

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Table des matières

III
1
IV
4
V
19
VI
33
VII
40
VIII
50
IX
52
X
54
XXXIV
186
XXXV
201
XXXVI
206
XXXVII
213
XXXVIII
220
XXXIX
230
XL
235
XLI
244

XI
58
XII
61
XIII
70
XIV
74
XV
76
XVII
82
XVIII
89
XX
102
XXI
107
XXII
111
XXIII
118
XXIV
123
XXV
127
XXVI
133
XXVII
138
XXVIII
149
XXIX
151
XXX
159
XXXI
176
XXXIII
177
XLII
251
XLIII
259
XLIV
263
XLVI
265
XLVII
279
XLVIII
289
XLIX
302
L
317
LI
324
LII
329
LIII
335
LIV
358
LV
371
LVI
383
LVII
396
LVIII
407
LIX
423
LX
431
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Fréquemment cités

Page 424 - Group theory and general relativity: representations of the Lorentz group and their applications to the gravitational field.
Page 425 - The conservation laws of nonrelativistic classical and quantum mechanics for a system of interacting particles «Helv.

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