等离子体流产生的电磁场和运动点电荷的Feynman和Lienard-Wiechert公式
Electromagnetic field generated by plasma flows and Feynman and Lienard-Wiechert formulas for a moving point charge
摘要：
本笔记代表了从发现运动点电荷产生的电磁场的精确数学公式（修正的费曼公式，见Bogdan arXiv：0909.5240）到狭义相对论洛伦兹框架中运动物质产生的引力场和电磁场的一般公式（Bogdan arXiv：0910.0538）的垫脚石。在本文中，作者介绍了洛伦兹框架中的物质流概念。这个概念在爱因斯坦的狭义相对论的意义上是相对论的。作者提出了明确的公式，适用于数字计算机允许一个找到时间延迟的行动，从流线中的任何一点的洛伦兹框架。在一个固定的洛伦兹坐标系中，任何等离子体流的时间延迟场都是唯一的。利用这个领域，他介绍了延迟时间场和基本领域的流动与自由参数表示的初始位置的线的流动。通过这些场，人们可以表示和建立波、洛伦兹规范、麦克斯韦方程组、Lienard-Wiechert势和修正的费曼公式之间的关系。在流量的初始位置上的电荷的初始分布由在Borel集上定义的有限变分的有符号测度给出。它可以包括离散和连续组件。
英文摘要：
This note represents a stepping stone from the discovery of the precise mathematical formula for electromagnetic field generated by a moving point charge, the amended Feynman formula, see Bogdan arXiv:0909.5240, and leading to the to the general formula of gravitational and electromagnetic fields generated by moving matter in a Lorentzian frame of special theory of relativity, Bogdan arXiv:0910.0538. In this note the author introduces the notion of flow of matter in a Lorentzian frame. This notion is relativistic in the sense of Einstein's special theory of relativity. The author presents explicit formulas suitable for a digital computer permitting one to find time delay for an action from a flow line to any point in the Lorentzian frame. The time delay field for any flow of plasma in a fixed Lorentzian frame is unique. Using this field he introduces the retarded time field and fundamental fields corresponding to the flow with a free parameter representing the initial positions of the lines of flow. By means of these fields one can represent and establish relations between wave, Lorentz gauge, and Maxwell equations, and Lienard-Wiechert potentials, and amended Feynman's formula. The initial distribution of charges over the initial position of the flow is given by a signed measure of finite variation defined over Borel sets. It may include discrete and continuous components.
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