球坐标中的分布及其在经典电动力学中的应用
Distributions in spherical coordinates with applications to classical electrodynamics
摘要：
提出了一种处理极坐标系原点奇点的一般而严格的方法。它的力量来自于径向距离和径向坐标变量之间的明确区别，这使得所有的δ函数及其导数都是自动生成的，并确保高斯定理对任何具有有限个孤立点状奇点的分布都是正确的。该方法被应用到库仑场，并显示在经典电动力学中的偶极子和双极场之间的内在差异。在所有情况下，该方法直接导致经典电动力学的内部一致性所需的一般表达式。
英文摘要：
A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that all delta-functions and their derivatives are automatically generated, and insures that the Gauss theorem is correct for any distribution with a finite number of isolated point-like singularities. The method is applied to the Coulomb field, and to show the intrinsic differences between the dipole and dimonopole fields in classical electrodynamics. In all cases the method directly leads to the general expressions required by the internal consistency of classical electrodynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
