2012/11/30 by Alexei A. Deriglazov, A. A. Deriglazov
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Bracket #Bundle #Fiber bundle #First class constraint #Geometry #Hamiltonian (control theory) #Hamiltonian mechanics #Helicity #Homogeneous space #Lie algebra #Lie group #Manifold (fluid mechanics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Phase space #Physics #Poisson algebra #Poisson bracket #Poisson manifold #Pure mathematics #Quantum #Quantum mechanics #Semiclassical physics #Symplectic geometry #Symplectic manifold #gr-qc #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1142/s0217732314500485
published as Modern Physics Letters A 29 (N 10) (2014) 1450048 (18 pages) · published version
openalex publication_date 2014/03/28 · arxiv created 2014/04/14 · arxiv updated 2014/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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".