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Topics in Contemporary Mathematical Physics

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Prefacep. vii
Vectors and Linear Transformationsp. 1
Tensorsp. 11
Symmetry and Conservation: the Angular Momentump. 19
The Angular Momentum as Generators of Rotations: Lie Groups and Lie Algebrasp. 25
Algebraic Structuresp. 37
Basic Group Conceptsp. 41
Basic Lie Algebra Conceptsp. 53
Inner Products, Metrics, and Dual Spacesp. 61
SO(4) and the Hydrogen Atomp. 71
Adjoints and Unitary Transformationsp. 79
The Lorentz Group and SL(2, C)p. 85
The Dirac Bracket Notation in Quantum Theoryp. 107
The Quantum Mechanical Simple Harmonic Oscillatorp. 113
Fourier Series and Fourier Transforms, the Dirac Delta Function, Green's Functionsp. 121
The Continuous Spectrum and Non-normalizable Statesp. 131
Skew-Symmetric Tensors and Determinantsp. 137
Eigenvalue Problemsp. 151
Group Representation Theoryp. 171
The Dihedral Group D[subscript 6] and the Benzene Moleculep. 191
Representations of the Symmetric Groups and the General Linear Groups, Young Diagramsp. 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 Harmonicsp. 247
The Structure of Semisimple Lie Algebrasp. 257
The Representations of Semisimple Lie Algebrasp. 277
SU(3) and the Strong Interactionp. 295
Clifford Algebrasp. 307
Exterior Productsp. 313
The Hodge-Star Operatorp. 323
Differential Forms and Exterior Differentiationp. 329
Moving Frames and Curvilinear Coordinates in R[superscript 3]p. 345
Integrals of Differential Forms and the Stokes Theoremp. 355
Homology and De Rham Cohomologyp. 371
The Geometry of Lie Groupsp. 379
Connections and Curvatures on a Vector Bundlep. 397
Yang-Mills Equationsp. 411
Connections on a Principal Bundlep. 417
Magnetic Monopoles and Molecular Dynamicsp. 447
Riemannian Geometryp. 463
Complex Manifoldsp. 491
Characteristic Classesp. 505
Chern-Simons Formsp. 533
The Atiyah-Singer Index Theoremp. 553
Symplectic Structures and Hamiltonian Mechanicsp. 575
Referencesp. 585
Table of Contents provided by Ingram. All Rights Reserved.

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