附註:Includes bibliographical references (pages 457-459) and index.
Cover -- Contents -- Preface -- 1. REVIEW ON LINEAR ALGEBRAS -- 1.1 Eigenvalues and Eigenvectors of a Matrix -- 1.2 Some Special Matrices -- 1.3 Similarity Transformation -- 2. GROUP AND ITS SUBSETS -- 2.1 Definition of a Group -- 2.2 Subsets in a Group -- 2.3 Homomorphism of Groups -- 3. THEORY OF REPRESENTATIONS -- 3.1 Transformation Operators for a Scalar Function -- 3.2 Inequivalent and Irreducible Representations -- 3.3 Subduced and Induced Representations -- 3.4 The Clebsch-Gardan Coefficients -- 4. THREE-DIMENSIONAL ROTATION GROUP -- 4.1 SO(3) Group and Its Covering Group SU(2) -- 4.2 Inequivalent and Irreducible Representations -- 4.3 Lie Groups and Lie Theorems -- 4.4 Irreducible Tensor Operators -- 4.5 Unitary Representations with Infinite Dimensions -- 5. SYMMETRY OF CRYSTALS -- 5.1 Symmetric Operations and Space Groups -- 5.2 Symmetric Elements -- 5.3 International Notations for Space Groups -- 6. PERMUTATION GROUPS -- 6.1 Multiplication of Permutations -- 6.2 Young Patterns, Young Tableaux and Young Operators -- 6.3 Primitive Idempotents in the Group Algebra -- 6.4 Irreducible Representations and Characters -- 6.5 The Inner and Outer Products of Representations -- 7. LIE GROUPS AND LIE ALGEBRAS -- 7.1 Classification of Semisimple Lie Algebras -- 7.2 Irreducible Representations and the Chevalley Bases -- 7.3 Reduction of the Direct Product of Representations -- 8. UNITARY GROUPS -- 8.1 The SU(N) Group and Its Lie Algebra -- 8.2 Irreducible Tensor Representations of SU(N) -- 8.3 Orthonormal Bases for Irreducible Representations -- 8.4 Subduced Representations -- 8.5 Casimir Invariants of SU(N) -- 9. REAL ORTHOGONAL GROUPS -- 9.1 Tensor Representations of SO(N) -- 9.2 Spinor Representations of SO(N) -- 9.3 SO(4) Group and the Lorentz Group -- 10. THE SYMPLECTIC GROUPS -- 10.1 The Groups Sp(2l, R) and USp(2l) -- 10.2 Irreducible Representations of Sp(2l) -- Bibliography -- Index.
摘要:"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 can be used by graduate students and young researchers in physics, especially theoretical physics. It is also suitable for some graduate students in theoretical chemistry."--Jacket.
