Motivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of generalized spinning particles on S2, the internal degrees of freedom of which are represented by a 3-vector obeying the structure relations of a three-dimensional real Lie algebra. Extensions 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 models, which rely upon real Lie algebras with dimensions d= 4 , 5 , 6 , is elucidated.
ASJC Scopus subject areas
- Engineering (miscellaneous)
- Physics and Astronomy (miscellaneous)