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    "Topics in Contemporary Mathematical Physics" by Kai S. Lam

    Posted By: exLib
    "Topics in Contemporary Mathematical Physics" by Kai S. Lam

    "Topics in Contemporary Mathematical Physics" by Kai S. Lam
    World Scientific Publishing | 2003 | ISBN: 9812384545 9789812384546 9789812384041 | 592 pages | PDF | 20 MB

    This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. The main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics.

    Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; (3) topology and differential geometry.

    The following are noteworthy features of this book:
    • the style of exposition is a fusion of those common in the standard physics and mathematics literatures;
    • the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience;
    • despite the diversity of the topics covered, there is a strong degree of thematic unity;
    • much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.

    Contents
    Preface
    1 Vectors and Linear Transformations
    2 Tensors
    3 Symmetry and Conservation: the Angular Momentum
    4 The Angular Momentum as Generators of Rotations: Lie Groups and Lie Algebras
    5 Algebraic Structures
    6 Basic Group Concepts
    7 Basic Lie Algebra Concepts
    8 Inner Products, Metrics, and Dual Spaces
    9 SO (4) and the Hydrogen Atom
    10 Adjoints and Unitary Transformations
    11 The Lorentz Group and SL(2, C)
    12 The Dirac Bracket Notation in Quantum Theory
    13 The Quantum Mechanical Simple Harmonic Oscillator
    14 Fourier Series and Fourier Transforms, the Dirac Delta Function, Green's Functions
    15 The Continuous Spectrum and Non-normalizable States
    16 Skew-Symmetric Tensors and Determinants
    17 Eigenvalue Problems
    18 Group Representation Theory
    19 The Dihedral Group D6 and the Benzene Molecule
    20 Representations of the Symmetric Groups and the General Linear Groups, Young Diagrams
    21 Irreducible Representations of U(n), SL{n), SU(n) and 0(n)
    22 Irreducible Representations of SU(2) and SO(3)
    23 The Spherical Harmonics
    24 The Structure of Semisimple Lie Algebras
    25 The Representations of Semisimple Lie Algebras
    26 SU(3) and the Strong Interaction
    27 Clifford Algebras
    28 Exterior Products
    29 The Hodge-Star Operator
    30 Differential Forms and Exterior Differentiation
    31 Moving Frames and Curvilinear Coordinates in R3
    32 Integrals of Differential Forms and the Stokes Theorem
    33 Homology and De Rham Cohomology
    34 The Geometry of Lie Groups
    35 Connections and Curvatures on a Vector Bundle
    36 Yang-Mills Equations
    37 Connections on a Principal Bundle
    38 Magnetic Monopoles and Molecular Dynamics
    39 Riemannian Geometry
    40 Complex Manifolds
    41 Characteristic Classes
    42 Chern-Simons Forms
    43 The Atiyah-Singer Index Theorem
    44 Symplectic Structures and Hamiltonian Mechanics
    References
    Index
    1st with TOC BookMarkLinks