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arXiv · 1211.1219

Variational problem for Hamiltonian system on so(k, m) Lie-Poisson manifold and dynamics of semiclassical spin

A. A. Deriglazov
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Abstract

We describe the procedure for obtaining Hamiltonian equations on a manifold with $so(k, m)$ Lie-Poisson bracket from a variational problem. This implies identification of the manifold with base of a properly constructed fiber bundle embedded as a surface into the phase space with canonical Poisson bracket. Our geometric construction underlies the formalism used for construction of spinning particles in [24-27], and gives precise mathematical formulation of the oldest idea about spin as the "inner angular momentum".

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A. A. Deriglazov. 2014-04-14. Variational problem for Hamiltonian system on so(k, m) Lie-Poisson manifold and dynamics of semiclassical spin. https://doi.org/10.1142/s0217732314500485

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