Holomorphy in Pseudo-Euclidean Spaces and the Classic Electromagnetic Theory

Vlad L. Negulescu
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Abstract

A new concept of holomorphy in pseudo-Euclidean spaces is briefly presented. The set of extended Cauchy-Riemannn differential equations, which are verified by the holomorphic functions, is obtained. A form of the general pseudo-rotation matrix was developed. The generalized d’Alembert- operator and extended Poisson’s equations are defined. Applying these results to the relativistic space-time, the charge conservation and general Maxwell equations are derived.
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伪欧几里德空间的全纯性与经典电磁理论
给出了伪欧几里德空间中全纯的一个新概念。得到了用全纯函数验证的扩展cauchy - riemann微分方程集。给出了一般伪旋转矩阵的一种形式。定义了广义达朗贝尔算子和扩展泊松方程。将这些结果应用于相对论时空,推导出电荷守恒方程和一般麦克斯韦方程。
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