Considerations on the electromagnetic field wave equation and the Dirac equation

TL;DR

This paper constructs a heuristic first-order wave equation for the electromagnetic field in vacuum and explores its formal similarity to the Dirac equation, providing insights into their mathematical relationship.

Contribution

It introduces a novel heuristic wave equation for electromagnetic fields and analyzes its formal analogy with the Dirac equation, offering new perspectives on their connection.

Findings

Established a heuristic electromagnetic wave equation in vacuum.

Identified formal similarities between the electromagnetic wave equation and the Dirac equation.

Provided a phenomenological basis for comparing electromagnetic and Dirac equations.

Abstract

Here is constructed a heuristic, first-order differential equation for the electromagnetic field in the vacuum, based on a phenomenological \textsl{ad hoc} argument. The formal similarity between this \textsl{ad hoc} wave equation and the Dirac equation is explored.