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The Poisson Algebra of the Classical Spin System

In: Symbol Correspondences for Spin Systems

Author

Listed:
  • Pedro de M. Rios

    (Universidade de São Paulo, Departamento de Matemática, ICMC)

  • Eldar Straume

    (Norwegian University of Science and Technology, Department of Mathematical Sciences)

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).

Suggested Citation

  • Pedro de M. Rios & Eldar Straume, 2014. "The Poisson Algebra of the Classical Spin System," Springer Books, in: Symbol Correspondences for Spin Systems, edition 127, chapter 0, pages 55-70, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-08198-4_4
    DOI: 10.1007/978-3-319-08198-4_4
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