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 | |
| Publication status | Published - 1 Jan 2014 |
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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
Cite this
Variational problem for Hamiltonian system on so(k, m)Lie-Poisson manifold and dynamics of semiclassical spin. / Deriglazov, A. A.
In: Modern Physics Letters A, Vol. 29, No. 10, 1450048, 01.01.2014.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Variational problem for Hamiltonian system on so(k, m)Lie-Poisson manifold and dynamics of semiclassical spin
AU - Deriglazov, A. A.
PY - 2014/1/1
Y1 - 2014/1/1
N2 - 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".
AB - 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".
KW - semiclassical models of spin
KW - Theories with Dirac constraints
KW - variational formulation on Lie-Poisson mani-folds
UR - http://www.scopus.com/inward/record.url?scp=84898474878&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84898474878&partnerID=8YFLogxK
U2 - 10.1142/S0217732314500485
DO - 10.1142/S0217732314500485
M3 - Article
VL - 29
JO - Modern Physics Letters A
JF - Modern Physics Letters A
SN - 0217-7323
IS - 10
M1 - 1450048
ER -