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 [A. A. Deriglazov, Mod. Phys. Lett. A 28, 1250234 (2013); Ann. Phys. 327, 398 (2012); Phys. Lett. A 376, 309 (2012)], and gives precise mathematical formulation of the oldest idea about spin as the "inner angular momentum".

Original language	English
Article number	1450048
Journal	Modern Physics Letters A
Volume	29
Issue number	10
DOIs	https://doi.org/10.1142/S0217732314500485
Publication status	Published - 1 Jan 2014

Keywords

semiclassical models of spin
Theories with Dirac constraints
variational formulation on Lie-Poisson mani-folds

ASJC Scopus subject areas

Nuclear and High Energy Physics
Astronomy and Astrophysics

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10.1142/S0217732314500485

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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 [A. A. Deriglazov, Mod. Phys. Lett. A 28, 1250234 (2013); Ann. Phys. 327, 398 (2012); Phys. Lett. A 376, 309 (2012)], and gives precise mathematical formulation of the oldest idea about spin as the {"}inner angular momentum{"}.",

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