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Classical and Quantum Mechanics via Lie algebras

  1. Oct 10, 2008 #1
    This is to announce the availability of a draft of a book
    Arnold Neumaier and Dennis Westra,
    Classical and Quantum Mechanics via Lie algebras,
    Cambridge University Press, to appear (2009?).
    (333 pages without references)
    Abstract and table of contents are given below.

    Your comments are welcome.
    Please send them to the newsgroup if they are of general interest,
    and to me directly otherwise.

    Arnold Neumaier


    The goal of this book is to present classical mechanics, quantum
    mechanics, and statistical mechanics in an almost completely algebraic
    setting, thereby introducing mathematicians, physicists, and
    engineers to the ideas relating classical and quantum mechanics with
    Lie algebras and Lie groups. The book emphasizes the
    closeness of classical and quantum mechanics, and the material is
    selected in a way to make this closeness as apparent as possible.

    Much of the material covered here is not part of standard
    textbook treatments of classical or quantum mechanics (or is only
    superficially treated there). For physics students who want to
    get a broader view of the subject, this book may therefore serve
    as a useful complement to standard treatments of quantum mechanics.

    Almost without exception, this book is about precise concepts and
    exact results in classical mechanics, quantum mechanics, and
    statistical mechanics. The structural properties of
    mechanics are discussed independent of computational techniques for
    obtaining quantitatively correct numbers from the assumptions made.
    The standard approximation machinery for calculating from first
    principles explicit thermodynamic properties of materials, or
    explicit cross sections for high energy experiments can be found in
    many textbooks and is not repeated here.


    Part I An invitation to quantum mechanics

    1 Motivation
    2 Classical oscillating systems
    3 Spectral analysis

    Part II Statistical mechanics

    4 Phenomenological thermodynamics
    5 Quantities, states and statistics
    6 The laws of thermodynamics
    7 Models, statistics, and measurements

    Part III Lie algebras and Poisson algebras

    8 Lie algebras
    9 Mechanics in Poisson algebras
    10 Representation and classification

    Part IV Mechanics and differential geometry

    11 Fields, forms, and derivatives
    12 Conservative mechanics on manifolds
    13 Hamiltonian quantum mechanics

    Part V Representations and spectroscopy

    14 Harmonic oscillators and coherent states
    15 Spin and fermions
    16 Highest weight representations
    17 Spectroscopy and spectra
  2. jcsd
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