A New Formulation of Electrodynamics

TL;DR

This paper introduces a novel mathematical formulation of electromagnetism using linear differential commutator brackets, deriving Maxwell's equations and the continuity equation within this new framework.

Contribution

It presents a new formalism based on differential commutator brackets to derive fundamental electromagnetism equations, offering a different mathematical perspective.

Findings

Maxwell's equations derived from the new formalism

Continuity equation expressed using differential commutator brackets

Provides a consistent mathematical framework for electromagnetism

Abstract

A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the Lorentz gauge connecting them. With the same formalism, the continuity equation is written in terms of these new differential commutator brackets. Keywords: Mathematical formulation, Maxwell's equations