Complex Form of Classical and Quantum Electrodynamics

TL;DR

This paper explores a complex covariant formulation of Maxwell's equations in moving media, deriving Lorentz invariant energy-momentum tensors and balance equations, laying groundwork for future discussions on conservation laws and quantization.

Contribution

It introduces a novel complex covariant form of Maxwell's equations and derives Lorentz invariant energy-momentum tensors for moving media.

Findings

Derived a compact Lorentz invariant energy-momentum tensor

Presented a covariant derivation of differential balance equations

Laid groundwork for future quantization and conservation law analysis

Abstract

We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, derivation of the energy-momentum tensor and the corresponding differential balance equations are given. Conservation laws and quantization of electromagnetic field will be discussed in this covariant approach elsewhere.