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

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".

published version

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Cited by in corpus (4)

• Frenkel electron and a spinning body in a curved background
• Lagrangian for the Frenkel electron
• World-line geometry probed by fast spinning particle
• Geometric Constructions Underlying Relativistic Description of Spin on the Base of Non-Grassmann Vector-Like Variable