扩展对称经典电动力学
Extended symmetrical classical electrodynamics
摘要：
在这篇文章中，我们讨论了经典电动力学的一个修改，其中“普通”点电荷缺席。修改后的方程包含描述感应电荷和电流的附加项。感应电荷和电流的密度取决于矢量k和电磁场E和B的矢量。结果表明，向量E和B可以用两个4-势来定义，并且k的分量是第三阶4-张量的分量。定义了修正电动力学的拉格朗日量。推导出只有一个四维势决定电磁场行为的条件。静态修正电动力学可以描述电介质内部的电磁场。在电场的外部区域，电场由麦克斯韦方程组控制。从在λ的内部区域和外部区域之间的界面处的边界条件得出，矢量k具有离散谱。对于不同的本征值k，得到了电介质的电场、磁场、能量和角动量。
英文摘要：
In the present article, we discuss a modification of classical electrodynamics in which ``ordinary'' point charges are absent. The modified equations contain additional terms describing the induced charges and currents. The densities of the induced charges and currents depend on the vector k and the vectors of the electromagnetic field E and B. It is shown that the vectors E and B can be defined in terms of two 4-potentials and the components of k are the components of the 4-tensor of the third rank. The Lagrangian of modified electrodynamics is defined. The conditions are derived at which only one 4-potential determines the behavior of the electromagnetic field. It is also shown that static modified electrodynamics can describe the electromagnetic field in the inner region of the electric monopole. In the outer region of the electric monopole the electric field is governed by the Maxwell equations. It follows from boundary conditions at the interface between the inner and outer regions of the monopole that the vector k has a discrete spectrum. The electric and magnetic fields, energy and angular momentum of the monopole are found for different eigenvalues of k.
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