论文标题
狄拉克磁性单极的可整合概括
Integrable generalisations of Dirac magnetic monopole
论文作者
论文摘要
我们用恒定磁场对拓扑球上的dirac磁单启动$ s^2 $上的某些集成（经典和量子）进行了分类，从而完成了Ferapontov，Sayles和Veselov的先前局部结果。 我们表明，有两个具有积分概括的概括家庭，它们在动量中是二次的。第一个家族对应于古典CLEBSCH系统，可以将其解释为谐波电场中的Dirac磁性单极。第二个家庭是新的，可以用Sphere $ S^2 $具有非常特殊的指标来编写。
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.
