This is to announce the availability of a draft of a book(adsbygoogle = window.adsbygoogle || []).push({});

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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