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Applications of the Theory of Groups in Mechanics and Physics

  • Book
  • © 2004

Overview

Authors:
  1. Petre P. Teodorescu

    1. Faculty of Mathematics, University of Bucharest, Bucharest, Romania

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  2. Nicolae-Alexandru P. Nicorovici

    1. School of Physics, The University of Sydney, Australia

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Fundamental Theories of Physics (FTPH, volume 140)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Elements of General Theory of Groups

    • Petre P. Teodorescu, Nicolae-Alexandru P. Nicorovici
    Pages 1-60

  3. Lie Groups

    • Petre P. Teodorescu, Nicolae-Alexandru P. Nicorovici
    Pages 61-121

  4. Symmetry Groups of Differential Equations

    • Petre P. Teodorescu, Nicolae-Alexandru P. Nicorovici
    Pages 123-200

  5. Applications in Mechanics

    • Petre P. Teodorescu, Nicolae-Alexandru P. Nicorovici
    Pages 201-277

  6. Applications in the Theory of Relativity and Theory of Classical Fields

    • Petre P. Teodorescu, Nicolae-Alexandru P. Nicorovici
    Pages 279-333

  7. Applications in Quantum Mechanics and Physics of Elementary Particles

    • Petre P. Teodorescu, Nicolae-Alexandru P. Nicorovici
    Pages 335-422

  8. Back Matter

    Pages 423-446
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Keywords

About this book

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.

Reviews

From the reviews:

"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)

Authors and Affiliations

  • Faculty of Mathematics, University of Bucharest, Bucharest, Romania

    Petre P. Teodorescu

  • School of Physics, The University of Sydney, Australia

    Nicolae-Alexandru P. Nicorovici

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