도서 정보
도서 상세설명
Preface
1 Vectors and Linear Transformations 1
2 Tensors 11
3 Symmetry and Conservation: the Angular Momentum 19
4 The Angular Momentum as Generators of Rotations: Lie Groups and Lie Algebras 25
5 Algebraic Structures 37
6 Basic Group Concepts 41
7 Basic Lie Algebra Concepts 53
8 Inner Products, Metrics, and Dual Spaces 61
9 SO(4) and the Hydrogen Atom 71
10 Adjoints and Unitary Transformations 79
11 The Lorentz Group and SL(2,C) 85
12 The Dirac Bracket Notation in Quantum Theory 107
13 The Quantum Mechanical Simple Harmonic Oscillator 113
14 Fourier Series and Fourier Transforms, the Dirac Delta Function, Green\'s Functions 121
15 The Continuous Spectrum and Non-normalizable States 131
16 Skew-Symmetric Tensors and Determinants 137
17 Eigenvalue Problems 151
18 Group Representation Theory 171
19 The Dihedral Group D[subscript 6] and the Benzene Molecule 191
20 Representations of the Symmetric Groups and the General Linear Groups, Young Diagrams 201
21 Irreducible Representations of U(n), SL(n), SU(n) and O(n) 219
22 Irreducible Representations of SU(2) and SO(3) 233
23 The Spherical Harmonics 247
24 The Structure of Semisimple Lie Algebras 257
25 The Representations of Semisimple Lie Algebras 277
26 SU(3) and the Strong Interaction 295
27 Clifford Algebras 307
28 Exterior Products 313
29 The Hodge-Star Operator 323
30 Differential Forms and Exterior Differentiation 329
31 Moving Frames and Curvilinear Coordinates in R[superscript 3] 345
32 Integrals of Differential Forms and the Stokes Theorem 355
33 Homology and De Rham Cohomology 371
34 The Geometry of Lie Groups 379
35 Connections and Curvatures on a Vector Bundle 397
36 Yang-Mills Equations 411
37 Connections on a Principle Bundle 417
38 Magnetic Monopoles and Molecular Dynamics 447
39 Riemannian Geometry 463
40 Complex Manifolds 491
41 Characteristic Classes 505
42 Chern-Simons Forms 533
43 The Atiyah-Singer Index Theorem 553
44 Symplectic Structures and Hamiltonian Mechanics 575
References 585
Index