Electromagnetic Lorenz Fields

TL;DR

This paper develops Lorenz field equations without gauge functions, revealing localized, light-like energy-carrying rays supported by polarization fields that are suppressed in traditional Maxwell fields due to gauge transformations.

Contribution

It introduces a nongauge Lorenz condition framework that uncovers emergent polarization fields and localized energy rays, expanding understanding of electromagnetic field structures.

Findings

Identification of three transformation classes relevant to Lorenz fields

Discovery of polarization fields supporting light-like energy rays

Localized rays are suppressed in standard Maxwell fields due to gauge choices

Abstract

Gauge transformations are potential transformations that leave only specific Maxwell fields invariant. To reveal more, I develop Lorenz field equations with full Maxwell form for nongauge, sans gauge function, transformations yielding mixed, superposed retarded and outgoing, potentials. The form invariant Lorenz condition is then a charge conservation equivalent. This allows me to define three transformation classes that screen for Lorenz relevance. The nongauge Lorentz conditions add polarization fields which support emergent, light-like rays that convey energy on charge conserving phase points. These localized rays escape discovery in modern Maxwell fields where the polarizations are suppressed by gauge transformations.