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Applications of the Theory of Groups in Mechanics and Physics: 140 (Fundamental Theories of Physics, 140) - Hardcover

 
9781402020469: Applications of the Theory of Groups in Mechanics and Physics: 140 (Fundamental Theories of Physics, 140)

Synopsis

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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"This book will be of interest for those readers aiming to have a view of the applications of group theory to several important questions in classical and quantum mechanics, as well as in the theory of differential equations. ... The amount of topics treated is ample, and each one is developed in detail ... so the book will be useful also for students. ... The book contains a number of cross references between material in different chapters, making the text clearer and self-consistent." (Arturo Ramos, Mathematical Reviews, Issue 2006 h)

"In the book a many of applications of the group theory to the solution and systematization of problems in the theory of differential equations, classical mechanics, relativity theory, quantum mechanics and elementary particle physics are presented. ... The book provides a simple introduction to the subject and requires as preliminaries only the mathematical knowledge acquired by a student in a technical university." (A. A. Bogush, Zentralblatt MATH, Vol. 1072 (23), 2005)

Synopsis

The present volume is a new edition of a volume published in 1985, ("Aplicatii ale teoriei grupurilor in mecanica si fizica", 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 Poincare groups of relativity theory).

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9789048165810: Applications of the Theory of Groups in Mechanics and Physics: 140 (Fundamental Theories of Physics, 140)

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Hardcover. Condition: new. Hardcover. We present applications of the group theory to the solution and systematization of several problems in the theory of differential equations (for instance, a base for the method of separation of variables), classical mechanics (for instance, the analytic form of the Lagrangian), relativity theory, quantum mechanics, and elementary particle physics. By this comprehensive work we wish to give the reader a number of preliminary notions and examples which are absolutely necessary for a better understanding of certain works, in different domains, which are based on applications of group theory. The present volume is a new edition of a volume published in 1985, ("Aplicatii ale teoriei grupurilor in mecanica si fizica", 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 Poincare groups of relativity theory). The work requires as preliminaries only the mathematical knowledge acquired by a student in a technical university. It is addressed to a large audience, to all those interested and compelled to use mathematical methods in various fields of research, such as mechanics, physics, engineering, people involved in research or teaching, as well as students. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781402020469

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