Ebook: Applications of the Theory of Groups in Mechanics and Physics

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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The present volume is a new edition of a volume published in 1985, ("Aplicatii ale teoriei grupurilor in mecanica si f?zica", Editura Tehnica, Bucharest, Romania). This new edition contains many improvements concerning the presentation, as well as new topics using an enlarged and updated bibliography.
In addition to the large area of domains in physics covered by this volume, we are presenting both discrete and continuous groups, while most of the books about applications of group theory in physics present only one type of groups (i.e., discrete or continuous), and the number of analyzed groups is also relatively small (i.e., point groups of crystallography, or the groups of rotations and translations as examples of continuous groups; some very specialized books study the Lorentz and Poincar? groups of relativity theory).

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The present volume is a new edition of a volume published in 1985, ("Aplicatii ale teoriei grupurilor in mecanica si f?zica", Editura Tehnica, Bucharest, Romania). This new edition contains many improvements concerning the presentation, as well as new topics using an enlarged and updated bibliography.
In addition to the large area of domains in physics covered by this volume, we are presenting both discrete and continuous groups, while most of the books about applications of group theory in physics present only one type of groups (i.e., discrete or continuous), and the number of analyzed groups is also relatively small (i.e., point groups of crystallography, or the groups of rotations and translations as examples of continuous groups; some very specialized books study the Lorentz and Poincar? groups of relativity theory).
Content:
Front Matter....Pages i-xiv
Elements of General Theory of Groups....Pages 1-60
Lie Groups....Pages 61-121
Symmetry Groups of Differential Equations....Pages 123-200
Applications in Mechanics....Pages 201-277
Applications in the Theory of Relativity and Theory of Classical Fields....Pages 279-333
Applications in Quantum Mechanics and Physics of Elementary Particles....Pages 335-422
Back Matter....Pages 423-446

---

The present volume is a new edition of a volume published in 1985, ("Aplicatii ale teoriei grupurilor in mecanica si f?zica", Editura Tehnica, Bucharest, Romania). This new edition contains many improvements concerning the presentation, as well as new topics using an enlarged and updated bibliography.
In addition to the large area of domains in physics covered by this volume, we are presenting both discrete and continuous groups, while most of the books about applications of group theory in physics present only one type of groups (i.e., discrete or continuous), and the number of analyzed groups is also relatively small (i.e., point groups of crystallography, or the groups of rotations and translations as examples of continuous groups; some very specialized books study the Lorentz and Poincar? groups of relativity theory).
Content:
Front Matter....Pages i-xiv
Elements of General Theory of Groups....Pages 1-60
Lie Groups....Pages 61-121
Symmetry Groups of Differential Equations....Pages 123-200
Applications in Mechanics....Pages 201-277
Applications in the Theory of Relativity and Theory of Classical Fields....Pages 279-333
Applications in Quantum Mechanics and Physics of Elementary Particles....Pages 335-422
Back Matter....Pages 423-446
....