Dirac磁链的可积推广
Integrable generalisations of Dirac magnetic monopole
摘要：
我们对具有常磁场的拓扑球$S^2$上Dirac磁链的某些可积（经典的和量子的）推广进行了分类，完成了Ferapontov，Sayles和Veselov以前的局部结果.我们表明，有两个可积的家庭，这样的概括与积分，这是二次动量。第一类对应于经典的Clebsch系统，它可以解释为谐电场中的Dirac磁共振。第二个家族是新的，可以写在球面$S^2$上的椭圆函数非常特殊的度量。
英文摘要：
We classify certain integrable (both classical and quantum) generalisations of Dirac magnetic monopole on topological sphere $S^2$ with constant magnetic field, completing the previous local results by Ferapontov, Sayles and Veselov. We show that there are two integrable families of such generalisations with integrals, which are quadratic in momenta. The first family corresponds to the classical Clebsch systems, which can be interpreted as Dirac magnetic monopole in harmonic electric field. The second family is new and can be written in terms of elliptic functions on sphere $S^2$ with very special metrics.
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