On a Connection between the Maxwell System, the Extended Maxwell System, the Dirac Operator and Gravito-Electromagnetism

TL;DR

This paper explores the deep mathematical connections between Maxwell's equations, Dirac's equation, and gravito-electromagnetism within the framework of evolutionary equations, revealing their structural similarities and applications to coupled systems.

Contribution

It demonstrates that Maxwell's, Dirac's, and gravito-electromagnetic equations are special cases of the extended Maxwell system, providing a unified analytical framework.

Findings

Unified representation of Maxwell, Dirac, and gravito-electromagnetic equations

Analysis of their formal relationships within evolutionary equations

Discussion of applications to coupled systems like Maxwell-Dirac

Abstract

Maxwell's equation, Dirac's equation and the equation of gravito-electromagnetism are shown to be particular instances of the extended Maxwell system. The equations are discussed in the framework of the theory of evolutionary equations. Their formal relationship are systematically analyzed. Applications to coupled systems such as the Maxwell-Dirac system are also discussed.