群论 英文

1 (p1): 1 Preface:the pursuit of symmetries
4 (p2): 2 Finite groups:an introduction
5 (p2-1): 2.1 Group axioms
6 (p2-2): 2.2 Finite groups of low order
19 (p2-3): 2.3 Permutations
22 (p2-4): 2.4 Basic concepts
22 (p2-4-1): 2.4.1 Conjugation
25 (p2-4-2): 2.4.2 Simple groups
27 (p2-4-3): 2.4.3 Sylow's criteria
28 (p2-4-4): 2.4.4 Semi-direct product
31 (p2-4-5): 2.4.5 Young Tableaux
33 (p3): 3 Finite groups:representations
33 (p3-1): 3.1 Introduction
35 (p3-2): 3.2 Schur's lemmas
41 (p3-3): 3.3 The A4 character table
44 (p3-4): 3.4 Kronecker products
46 (p3-5): 3.5 Real and complex representations
48 (p3-6): 3.6 Embeddings
52 (p3-7): 3.7 Zn character table
53 (p3-8): 3.8 Dn character table
56 (p3-9): 3.9 Q2n character table
58 (p3-10): 3.10 Some semi-direct products
61 (p3-11): 3.11 Induced representations
64 (p3-12): 3.12 Invariants
67 (p3-13): 3.13 Coverings
69 (p4): 4 Hilbert spaces
69 (p4-1): 4.1 Finite Hilbert spaces
70 (p4-2): 4.2 Fermi oscillators
72 (p4-3): 4.3 Infinite Hilbert spaces
78 (p5): 5 SU(2)
78 (p5-1): 5.1 Introduction
82 (p5-2): 5.2 Some representations
86 (p5-3): 5.3 From Lie algebras to Lie groups
89 (p5-4): 5.4 SU(2)→SU(1,1)
93 (p5-5): 5.5 Selected SU(2)applications
93 (p5-5-1): 5.5.1 The isotropic harmonic oscillator
95 (p5-5-2): 5.5.2 The Bohr atom
99 (p5-5-3): 5.5.3 Isotopic spin
102 (p6): 6 SU(3)
102 (p6-1): 6.1 SU(3)algebra
106 (p6-2): 6.2 α-Basis
107 (p6-3): 6.3 ω-Basis
108 (p6-4): 6.4 α′-Basis
110 (p6-5): 6.5 The triplet representation
112 (p6-6): 6.6 The Chevalley basis
114 (p6-7): 6.7 SU(3)in physics
114 (p6-7-1): 6.7.1 The isotropic harmonic oscillator redux
115 (p6-7-2): 6.7.2 The Elliott model
117 (p6-7-3): 6.7.3 The Sakata model
118 (p6-7-4): 6.7.4 The Eightfold Way
123 (p7): 7 Classification of compact simple Lie algebras
124 (p7-1): 7.1 Classification
129 (p7-2): 7.2 Simple roots
131 (p7-3): 7.3 Rank-two algebras
134 (p7-4): 7.4 Dynkin diagrams
140 (p7-5): 7.5 Orthonormal bases
143 (p8): 8 Lie algebras:representation theory
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