Groups and Symmetries: From Finite Groups to Lie Groups (Universitext) - Softcover

Kosmann-Schwarzbach, Yvette

9780387788654: Groups and Symmetries: From Finite Groups to Lie Groups (Universitext)

Softcover

ISBN 10: 0387788654 ISBN 13: 9780387788654

Publisher: Springer, 2009

Beginning with a review of the basic definitions and results of group theory, this volume illustrates definitions with examples important to the study of symmetry. With only linear algebra and calculus as prerequisites, this book will be widely accessible.

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Review:

From the reviews:

“Groups and Symmetries is a short, concise book ... that provides an introduction to the subject of Lie Groups, Lie Algebras, their representations, and their uses in theoretical particle physics. ... Anyone interested in understanding the connection between quarks and representation theory is an expeditious fashion should read this book. ... at the end of each chapter, Groups and Symmetries has a helpful reference section that provides readers with historical comments and additional references to the topics covered.” (Thomas R. Hagedorn, The Mathematical Association of America, April, 2010)

“This book by Kosmann-Schwarzbach (�cole Polytechnique, France) also starts with the basics but rapidly moves on to enrich group theory with notions from topology, analysis, and (multi) linear algebra. Surely one finds many monographs on Lie groups for students on the way to specializing. ... Summing Up: Recommended. Upper-division undergraduates, graduate students, and professionals.” (D. V. Feldman, Choice, Vol. 47 (11), July, 2010)

“This book gives a gentle introduction to the theory of group representations and its applications in quantum mechanics. ... This book is well written and is well suited for a course aimed at advanced undergraduates and early graduate students.” (Aloysius Helminck, Mathematical Reviews, Issue 2011 g)

“The author gives a very clear and comprehensible introduction to the representation theory of groups focussing in particular on Lie groups. ... A series of nine problems and solutions completes this well thought-out and well organized book, which can be recommended already to advanced undergraduates.” (G. Kowol, Monatshefte f�r Mathematik, Vol. 164 (2), October, 2011)

Synopsis:

The theory of group representations is an elegant subject at the intersection of algebra, geometry, and analysis, with applications to crystallography and the physics of atomic and subatomic particles. This book is an introduction to both the theory and applications of group representations. The author lends coherence to this vast subject by focusing on the connections between group representations and the study of symmetry. The book begins with a brisk review of the basic definitions and fundamental results of group theory.Definitions are illustrated with examples important to the study of symmetry, such as the symmetric group and the Lie groups SU(2) and SO(3). The representation theory of finite groups is introduced in Chapter 2, and the principal results generalized to compact groups in Chapter 3. In later chapters Lie algebras and Lie groups are introduced, with the Lie groups SU(2) and SO(3) and their representations studied in detail. Chapter 7 on spherical harmonics connects SO(3) to applications in electrodynamics and quantum mechanics, while Chapter 8 applies SU(3) to the study of quarks.

With only linear algebra and calculus as prerequisites, this book will be accessible to both advanced undergraduates and beginning graduate students. An extensive collection of exercises, many with answers or complete solutions, makes this an ideal text for the classroom or independent study.

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