Some Arguments for the Wave Equation in Quantum Theory 2

TL;DR

This paper explores conditions under which charges and currents in quantum theory frames either vanish or satisfy wave equations, linking non-radiating frames to wave equation solutions in relativistic settings.

Contribution

It establishes a connection between non-radiating frames and wave equations for charges and currents, extending previous results to analytic cases in quantum theory.

Findings

Non-radiating frames imply vanishing charges and currents or wave equation satisfaction.

Analytic charges and currents lead to specific wave equation solutions in all related frames.

The results extend the understanding of wave behavior in quantum non-radiating systems.

Abstract

We prove that if the frame S is decaying surface non-radiating, in the sense of Definition 1.1, then if the charge and current are analytic, either they both vanish, or S is non-radiating, in the sense of a previous paper. In particularly, by the result there, the charge and current satisfy certain wave equations in all frames S', connected to S by a real velocity vector, whose magnitude is less than the speed of light.