Electromagnetic field generated by plasma flows and Feynman and Lienard-Wiechert formulas for a moving point charge

TL;DR

This paper develops explicit formulas for electromagnetic fields generated by plasma flows in a Lorentzian frame, extending Feynman's and Lienard-Wiechert formulas, and introduces the notion of matter flow in special relativity.

Contribution

It introduces a relativistic notion of matter flow, provides computable formulas for time delay and retarded time fields, and relates these to fundamental electromagnetic equations.

Findings

Unique time delay field for plasma flows in Lorentzian frames

Explicit formulas for retarded time and fundamental fields

Relations established between wave, Maxwell, and Lienard-Wiechert potentials

Abstract

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.