Abstract
We describe geometric construction underlying the Lagrangian actions for non-Grassmann spinning particles proposed in our recent works. If we discard the spatial variables (the case of frozen spin), the problem reduces to formulation of a variational problem for Hamiltonian system on a manifold with so(n) Lie-Poisson bracket. To achieve this, we identify dynamical variables of the problem with coordinates of the base of a properly constructed fiber bundle. In turn, the fiber bundle is embedded as a surface into the phase space equipped with canonical Poisson bracket. This allows us to formulate the variational problem using the standard methods of Dirac theory for constrained systems.
| Original language | English |
|---|---|
| Article number | 012011 |
| Journal | Journal of Physics: Conference Series |
| Volume | 411 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2013 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Kinematics of semiclassical spin and spin fiber bundle associated with so(n) Lie-Poisson manifold. / Deriglazov, A. A.
In: Journal of Physics: Conference Series, Vol. 411, No. 1, 012011, 2013.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Kinematics of semiclassical spin and spin fiber bundle associated with so(n) Lie-Poisson manifold
AU - Deriglazov, A. A.
PY - 2013
Y1 - 2013
N2 - We describe geometric construction underlying the Lagrangian actions for non-Grassmann spinning particles proposed in our recent works. If we discard the spatial variables (the case of frozen spin), the problem reduces to formulation of a variational problem for Hamiltonian system on a manifold with so(n) Lie-Poisson bracket. To achieve this, we identify dynamical variables of the problem with coordinates of the base of a properly constructed fiber bundle. In turn, the fiber bundle is embedded as a surface into the phase space equipped with canonical Poisson bracket. This allows us to formulate the variational problem using the standard methods of Dirac theory for constrained systems.
AB - We describe geometric construction underlying the Lagrangian actions for non-Grassmann spinning particles proposed in our recent works. If we discard the spatial variables (the case of frozen spin), the problem reduces to formulation of a variational problem for Hamiltonian system on a manifold with so(n) Lie-Poisson bracket. To achieve this, we identify dynamical variables of the problem with coordinates of the base of a properly constructed fiber bundle. In turn, the fiber bundle is embedded as a surface into the phase space equipped with canonical Poisson bracket. This allows us to formulate the variational problem using the standard methods of Dirac theory for constrained systems.
UR - http://www.scopus.com/inward/record.url?scp=84874133257&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84874133257&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/411/1/012011
DO - 10.1088/1742-6596/411/1/012011
M3 - Article
VL - 411
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
IS - 1
M1 - 012011
ER -