arXiv 2007.102852020-07physics.class-phphysics.hist-ph

电磁场的洛仑兹条件和麦克斯韦系统的适用条件

Condición de Lorentz y ecuaciones de ondas electromagnéticas como propiedades emergentes del sistema de Maxwell

Yudier Peña Pérez, Juan Bory Reyes

备注：: in Spanish. The sections were organized in a better way. Revised argument in section 4, results unchanged. The reference list has been updated

摘要：

本文从系统论的角度研究麦克斯韦系统的涌现性质，即电磁波方程和洛仑兹条件。为此，首先推导了波动方程和亥姆霍兹方程。利用与主要矢量计算算子密切相关的位移狄拉克算子，可以在麦克斯韦时谐方程组的解和两个四元数方程之间建立直接联系。此外，应用洛伦兹条件将时谐麦克斯韦系统转化为一个简单的基于标量和矢量势的四元数方程。

英文摘要：

This article deals with the study of electromagnetic waves equations and the Lorentz condition, as emergent properties of Maxwell's system in the context of systems theory. To do this, the wave equations and the Helmholtz equation are first deduced. Using the displaced Dirac operator, which is closely related to the main vector calculation operators, it is possible to establish a direct connection between the solutions of the Maxwell time-harmonic system and two quaternion equations. Also, the application of the Lorentz condition to transform the time-harmonic Maxwell system into a simple quaternion equation based on the scalar and vector potentials is exposed.

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