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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)