标题： 沿Bianchi分类的2球面上的自旋粒子 显示英文标题

标题： Spinning particles on 2-sphere in accord with the Bianchi classification

摘要： 受最近关于扩展了自旋自由度的超共形力学研究的启发，我们构建了二维球面上自旋粒子的极小超可积模型，其中自旋自由度由满足三维实李代数结构关系的三维矢量表示。 讨论了涉及外部场（如狄拉克磁单极场）、SU(2) 群流形上的运动，或者产生两个二次运动守恒量的标量势的推广情况。 阐明了一种基于 d=4,5,6 实李代数构建类似扩展的方法。 显示英文摘要

摘要： 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.