The Poisson Algebra of the Classical Spin System

Pedro de M. Rios and Eldar Straume
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Pedro de M. Rios: Universidade de São Paulo, Departamento de Matemática, ICMC
Eldar Straume: Norwegian University of Science and Technology, Department of Mathematical Sciences

Chapter Chapter 4 in Symbol Correspondences for Spin Systems, 2014, pp 55-70 from Springer

Abstract: Abstract This chapter presents the basic mathematical framework for classical mechanics of a spin system. Practically all the material in the introductory section below can be found in basic textbooks on classical mechanics and we refer to some of these, e.g. [1, 5, 34, 37, 48], for the reader not yet too familiar with the subject, or for further details, examples, etc. (Ref. [34] is more familiar to physicists, while the others are more mathematical and closer in style to our brief introduction below). Our emphasis here is to provide a self-contained presentation of the SO(3)-invariant decomposition of the pointwise product and the Poisson bracket of polynomials, which are not easily found elsewhere (specially the latter).

Keywords: Poisson Bracket; Symplectic Form; Symplectic Manifold; Poisson Algebra; Coadjoint Orbit (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-08198-4_4

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