Group Theory in Physics, Volume 1

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World Scientific, 1985 - Science - 344 pages
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An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems.Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry.Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained.A set of problems and solutions has been published in a separate booklet.
 

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Contents

INTRODUCTION I
1
BASIC GROUP THEORY
12
GROUP REPRESENTATIONS
27
GENERAL PROPERTIES OF IRREDUCIBLE
54
REPRESENTATIONS OF THE SYMMETRIC
64
ONEDIMENSIONAL CONTINUOUS GROUPS
80
ROTATIONS IN THREEDIMENSIONAL
94
THE GROUP SU2 AND MORE ABOUT SO3
125
SPACE INVERSION INVARIANCE
212
Parity
238
TIME REVERSAL INVARIANCE
245
FINITEDIMENSIONAL REPRESENTATIONS
262
NOTATIONS AND SYMBOLS
292
GROUP ALGEBRA AND THE REDUCTION
307
SUPPLEMENTS TO THE THEORY
314
ROTATIONAL AND LORENTZ SPINORS
320

EUCLIDEAN GROUPS IN TWO
152
THE LORENTZ AND POINCARE GROUPS
173
Transformations
179
UNITARY REPRESENTATIONS OF
328
REFERENCES AND BIBLIOGRAPHY
335
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