麦克斯韦方程的几何表述法

The geometric representation of Maxwell's equation

本文在采用微分几何中的度量与外导数概念的基础上,借助于法拉第张量及完全自由的坐标系统,给出了麦克斯韦方程在任何流形中都具有的更为简化和更为普遍的几何表述形式,给出了电荷是一种拓扑结构的几何意义,同时也给电荷的定义一种新的解释;并探讨了在磁单极子存在时的麦克斯韦方程的几何形式.最后通过对矢势与平面电磁波的讨论,证明了由几何表述所导出的结论与用微分表述所得结论完全一致,且前者给出了较后者更为清晰简明的几何图象.

Based on the measurement and the outer derivative concept of differential geometry , by the aid of Faraday tensor and completely free coordinate system this article presented a more simple and more general geometric representation of Maxwell's equation in any manifold and the geometric meaning of electricity as a topological structure , unfolded the secret of electricity , discussed the geometric form of Maxwell's equation when there are magnetic single poles. Lastly, through the discussion of vector potential and plane electromagnetic wave,it proved that the conclusion from geometric representation and the conclusion from differential representation are completely same moreover, it presented a geometric picture which is clearer and more simple than that of differential representation.