Regular Article – Theoretical Physics
Generalized spinning particles on in accord with the Bianchi classification
Tomsk Polytechnic University, Lenin Ave. 30, 634050, Tomsk, Russia
2 Tomsk State University of Control Systems and Radioelectronics, 634050, Tomsk, Russia
Accepted: 20 February 2021
Published online: 2 March 2021
Motivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of generalized spinning particles on , 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 , is elucidated.
© The Author(s) 2021
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