Spinning particles on 2-sphere in accord with the Bianchi classification
High Energy Physics - Theory
2021-03-17 v1 Exactly Solvable and Integrable Systems
Abstract
Motivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of spinning particles on 2-sphere, the spin degrees of freedom of which are represented by a 3-vector obeying the structure relations of a 3d real Lie algebra. Generalisations involving an external field of the Dirac monopole, or the motion on the group manifold of SU(2), or a scalar potential giving rise to two quadratic constants of the motion are discussed. A procedure how to build similar extensions, which rely upon d=4,5,6 real Lie algebras, is elucidated.
Cite
@article{arxiv.2012.01054,
title = {Spinning particles on 2-sphere in accord with the Bianchi classification},
author = {Anton Galajinsky},
journal= {arXiv preprint arXiv:2012.01054},
year = {2021}
}
Comments
13 pages