1211.1219 (A. A. Deriglazov)

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

A. A. Deriglazov

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 \cite{AAD2, AAD3, AAD7, AAD4}, and gives precise mathematical formulation of the oldest idea about spin as the "inner angular momentum".

View original: http://arxiv.org/abs/1211.1219