Overview

"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."

Full Product Details

Author:   Petre P. Teodorescu ,  Nicolae-A.P. Nicorovici
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2004 ed.
Volume:   140
Dimensions:   Width: 15.60cm , Height: 2.50cm , Length: 23.40cm
Weight:   0.874kg
ISBN:  

9781402020469

ISBN 10:   1402020465
Pages:   446
Publication Date:   30 April 2004
Audience:   General/trade ,  College/higher education ,  General ,  Tertiary & Higher Education
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

1. Elements of General Theory of Groups.- 1 Basic notions.- 2 Topological groups.- 3 Particular Abelian groups.- 2. Lie Groups.- 1 The SO(3) group.- 2 The SU(2) group.- 3 The SU(3) and GL(n, ?) groups.- 4 The Lorentz group.- 3. Symmetry Groups of Differential Equations.- 1 Differential operators.- 2 Invariants and differential equations.- 3 Symmetry groups of certain differential equations.- 4 Methods of study of certain differential equations.- 4. Applications in Mechanics.- 1 Classical models of mechanics.- 2 Symmetry laws and applications.- 3 Space-time symmetries. Conservation laws.- 4 Applications in the theory of vibrations.- 5. Applications in the Theory of Relativity and Theory of Classical Fields.- 1 Theory of Special Relativity.- 2 Theory of electromagnetic field.- 3 Theory of gravitational field.- 6. Applications in Quantum Mechanics and Physics of Elementary Particles.- 1 Non-relativistic quantum mechanics.- 2 Internal symmetries of elementary particles.- 3 Relativistic quantum mechanics.- References.

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)

From the reviews: <p> 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. a ] The amount of topics treated is ample, and each one is developed in detail a ] so the book will be useful also for students. a ] 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) <p> 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)

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