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Preface | p. vii |
Vectors and Linear Transformations | p. 1 |
Tensors | p. 11 |
Symmetry and Conservation: the Angular Momentum | p. 19 |
The Angular Momentum as Generators of Rotations: Lie Groups and Lie Algebras | p. 25 |
Algebraic Structures | p. 37 |
Basic Group Concepts | p. 41 |
Basic Lie Algebra Concepts | p. 53 |
Inner Products, Metrics, and Dual Spaces | p. 61 |
SO(4) and the Hydrogen Atom | p. 71 |
Adjoints and Unitary Transformations | p. 79 |
The Lorentz Group and SL(2, C) | p. 85 |
The Dirac Bracket Notation in Quantum Theory | p. 107 |
The Quantum Mechanical Simple Harmonic Oscillator | p. 113 |
Fourier Series and Fourier Transforms, the Dirac Delta Function, Green's Functions | p. 121 |
The Continuous Spectrum and Non-normalizable States | p. 131 |
Skew-Symmetric Tensors and Determinants | p. 137 |
Eigenvalue Problems | p. 151 |
Group Representation Theory | p. 171 |
The Dihedral Group D[subscript 6] and the Benzene Molecule | p. 191 |
Representations of the Symmetric Groups and the General Linear Groups, Young Diagrams | p. 201 |
Irreducible Representations of U(n), SL(n), SU(n) and O(n) | p. 219 |
Irreducible Representations of SU(2) and SO(3) | p. 233 |
The Spherical Harmonics | p. 247 |
The Structure of Semisimple Lie Algebras | p. 257 |
The Representations of Semisimple Lie Algebras | p. 277 |
SU(3) and the Strong Interaction | p. 295 |
Clifford Algebras | p. 307 |
Exterior Products | p. 313 |
The Hodge-Star Operator | p. 323 |
Differential Forms and Exterior Differentiation | p. 329 |
Moving Frames and Curvilinear Coordinates in R[superscript 3] | p. 345 |
Integrals of Differential Forms and the Stokes Theorem | p. 355 |
Homology and De Rham Cohomology | p. 371 |
The Geometry of Lie Groups | p. 379 |
Connections and Curvatures on a Vector Bundle | p. 397 |
Yang-Mills Equations | p. 411 |
Connections on a Principal Bundle | p. 417 |
Magnetic Monopoles and Molecular Dynamics | p. 447 |
Riemannian Geometry | p. 463 |
Complex Manifolds | p. 491 |
Characteristic Classes | p. 505 |
Chern-Simons Forms | p. 533 |
The Atiyah-Singer Index Theorem | p. 553 |
Symplectic Structures and Hamiltonian Mechanics | p. 575 |
References | p. 585 |
Table of Contents provided by Ingram. All Rights Reserved. |
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