Problems & Solutions in Group Theory for Physicists,9789812388339

Problems & Solutions in Group Theory for Physicists

by ;
ISBN13: 9789812388339
ISBN10: 9812388338
Format: Paperback
Pub. Date: 2004-08-01
Publisher(s): World Scientific Pub Co Inc
List Price: $28.00

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Summary

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.

Table of Contents

Preface v
1. REVIEW ON LINEAR ALGEBRAS
1(26)
1.1 Eigenvalues and Eigenvectors of a Matrix
1(3)
1.2 Some Special Matrices
4(3)
1.3 Similarity Transformation
7(20)
2. GROUP AND ITS SUBSETS
27(16)
2.1 Definition of a Group
27(2)
2.2 Subsets in a Group
29(4)
2.3 Homomorphism of Groups
33(10)
3. THEORY OF REPRESENTATIONS
43(72)
3.1 Transformation Operators for a Scalar Function
43(4)
3.2 Inequivalent and Irreducible Representations
47(18)
3.3 Subduced and Induced Representations
65(14)
3.4 The Clebsch-Gordan Coefficients
79(36)
4. THREE-DIMENSIONAL ROTATION GROUP
115(58)
4.1 SO(3) Group and Its Covering Group SU(2)
115(8)
4.2 Inequivalent and Irreducible Representations
123(17)
4.3 Lie Groups and Lie Theorems
140(6)
4.4 Irreducible Tensor Operators
146(20)
4.5 Unitary Representations with Infinite Dimensions
166(7)
5. SYMMETRY OF CRYSTALS
173(20)
5.1 Symmetric Operations and Space Groups
173(4)
5.2 Symmetric Elements
177(9)
5.3 International Notations for Space Groups
186(7)
6. PERMUTATION GROUPS
193(76)
6.1 Multiplication of Permutations
193(4)
6.2 Young Patterns, Young Tableaux and Young Operators
197(8)
6.3 Primitive Idempotents in the Group Algebra
205(6)
6.4 Irreducible Representations and Characters
211(26)
6.5 The Inner and Outer Products of Representations
237(32)
7. LIE GROUPS AND LIE ALGEBRAS
269(48)
7.1 Classification of Semisimple Lie Algebras
269(10)
7.2 Irreducible Representations and the Chevalley Bases
279(20)
7.3 Reduction of the Direct Product of Representations
299(18)
8. UNITARY GROUPS
317(58)
8.1 The SU(N) Group and Its Lie Algebra
317(4)
8.2 Irreducible Tensor Representations of SU(N)
321(15)
8.3 Orthonormal Bases for Irreducible Representations
336(26)
8.4 Subduced Representations
362(7)
8.5 Casimir Invariants of SU(N)
369(6)
9. REAL ORTHOGONAL GROUPS
375(58)
9.1 Tensor Representations of SO(N)
375(28)
9.2 Spinor Representations of SO(N)
403(12)
9.3 SO(4) Group and the Lorentz Group
415(18)
10. THE SYMPLECTIC GROUPS 433(24)
10.1 The Groups Sp(2l, R) and USp(2l)
433(7)
10.2 Irreducible Representations of Sp(2l)
440(17)
Bibliography 457(4)
Index 461

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