Applications of the Theory of Groups in Mechanics and Physics

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Springer Science & Business Media, Apr 30, 2004 - Mathematics - 446 pages
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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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Contents

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

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