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Problems and Solutions in Group Theory for Physicists - Zhong-Qi Ma

Problems and Solutions in Group Theory for Physicists

Paperback Published: 8th June 2004
ISBN: 9789812388339
Number Of Pages: 476

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This book is aimed at graduate students in physics who are studying group theory and its application to physics. It contains a short explanation of the fundamental knowledge and method, and the fundamental exercises for the method, as well as some important conclusions in group theory. The book has been designed as a supplement to the author's textbook Group Theory for Physicists, also published by World Scientific. Together these two books can be used in a course on group theory for first-year graduate students in physics, especially theoretical physics. They are also suitable for some graduate students in theoretical chemistry.

?The authors present an interesting book explaining group theory in terms of physics ..."

Prefacep. v
Review on Linear Algebrasp. 1
Eigenvalues and Eigenvectors of a Matrixp. 1
Some Special Matricesp. 4
Similarity Transformationp. 7
Group and Its Subsetsp. 27
Definition of a Groupp. 27
Subsets in a Groupp. 29
Homomorphism of Groupsp. 33
Theory of Representationsp. 43
Transformation Operators for a Scalar Functionp. 43
Inequivalent and Irreducible Representationsp. 47
Subduced and Induced Representationsp. 65
The Clebsch-Gordan Coefficientsp. 79
Three-Dimensional Rotation Groupp. 115
SO(3) Group and Its Covering Group SU(2)p. 115
Inequivalent and Irreducible Representationsp. 123
Lie Groups and Lie Theoremsp. 140
Irreducible Tensor Operatorsp. 146
Unitary Representations with Infinite Dimensionsp. 166
Symmetry of Crystalsp. 173
Symmetric Operations and Space Groupsp. 173
Symmetric Elementsp. 177
International Notations for Space Groupsp. 186
Permutation Groupsp. 193
Multiplication of Permutationsp. 193
Young Patterns, Young Tableaux and Young Operatorsp. 197
Primitive Idempotents in the Group Algebrap. 205
Irreducible Representations and Charactersp. 211
The Inner and Outer Products of Representationsp. 237
Lie Groups and Lie Algebrasp. 269
Classification of Semisimple Lie Algebrasp. 269
Irreducible Representations and the Chevalley Basesp. 279
Reduction of the Direct Product of Representationsp. 299
Unitary Groupsp. 317
The SU(N) Group and Its Lie Algebrap. 317
Irreducible Tensor Representations of SU(N)p. 321
Orthonormal Bases for Irreducible Representationsp. 336
Subduced Representationsp. 362
Casimir Invariants of SU(N)p. 369
Real Orthogonal Groupsp. 375
Tensor Representations of SO(N)p. 375
Spinor Representations of SO(N)p. 403
SO(4) Group and the Lorentz Groupp. 415
The Symplectic Groupsp. 433
The Groups Sp(2l, R) and USp(2l)p. 433
Irreducible Representations of Sp(2l)p. 440
Bibliographyp. 457
Indexp. 461
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9789812388339
ISBN-10: 9812388338
Audience: General
Format: Paperback
Language: English
Number Of Pages: 476
Published: 8th June 2004
Country of Publication: SG
Dimensions (cm): 22.45 x 15.39  x 2.39
Weight (kg): 0.66