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Classical and Quantum Mechanics via Lie algebras 
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Oct1008, 05:00 AM

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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?). arXiv:0810.1019 http://lanl.arxiv.org/abs/0810.1019 (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 


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