磁单极子和双子的再认识：对经典力学研究的有益贡献
Magnetic monopoles and dyons revisited: A useful contribution to the study of classical mechanics
摘要：
世界上许多国家的研究生水平的物理课程，以及一些主要机构的高级本科课程，包括经典力学课程，主要基于戈尔茨坦的教科书杰作。然而，在讨论有心力运动时，开普勒问题实际上是唯一的严肃应用。在本文中，我们提出了另一个问题，也是可溶性的，即Schwinger的双电荷（双子）粒子的相互作用。虽然磁单极子和电荷的电磁相互作用的详细研究了大约40年前，我们认为，从本质上经典力学的角度来看，它的教学讨论是一个有益的贡献，为学生。以下的路径，概括开普勒的问题和卢瑟福散射，我们表明，他们表现出显着的属性，如稳定的非平面轨道，以及彩虹和荣耀散射，这是不存在于普通的两个单带电粒子的散射。此外，它可以进一步扩展到相对论的情况和半经典量子化，这也可以包括在课堂讨论中。
英文摘要：
Graduate level physics curricula in many countries around the world, as well as senior-level undergraduate ones in some major institutions, include Classical Mechanics courses, mostly based on Goldstein's textbook masterpiece. During the discussion of central force motion, however, the Kepler problem is virtually the only serious application presented. In this paper, we present another problem that is also soluble, namely the interaction of Schwinger's dual-charged (dyon) particles. While the electromagnetic interaction of magnetic monopoles and electric charges was studied in detail some 40 years ago, we consider that a pedagogical discussion of it from an essentially classical mechanics point of view is a useful contribution for students. Following a path that generalizes Kepler's problem and Rutherford scattering, we show that they exhibit remarkable properties such as stable non-planar orbits, as well as rainbow and glory scattering, which are not present in the ordinary scattering of two singly charged particles. Moreover, it can be extended further to the relativistic case and to a semi-classical quantization, which can also be included in the class discussion.
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