Riemann-Silberstein representation of the complete Maxwell equations set

TL;DR

This paper presents a unified Riemann-Silberstein vector formulation of Maxwell's equations, deriving gauge conditions and linking invariants to electromagnetic power dissipation.

Contribution

It introduces a single-equation representation of Maxwell's equations using Riemann-Silberstein vectors and derives related gauge and invariant properties.

Findings

Fourier invariants relate to dissipated power

Invariants ${f EB}$ and $E^{2}-B^{2}$ have specific physical interpretations

Unified complex vector formulation simplifies Maxwell's equations

Abstract

The complete set of Maxwell equations is represented by a single equation using Riemann-Silberstein complex vector of electromagnetic field. The consistent derivation of the Lorenz gauge condition is presented. We demonstrate that Fourier form of invariants ${\bf EB}$ and $E^{2}-B^{2}$ are proportional to dissipated power and equal to zero respectively.