On the energy-momentum current of the electromagnetic field in a pre-metric axiomatic approach. I

TL;DR

This paper develops a metric-free axiomatic framework for electrodynamics by defining and analyzing the properties of the electromagnetic energy-momentum current, emphasizing its invariance, symmetry, and tracelessness.

Contribution

It introduces the electromagnetic energy-momentum current within a pre-metric axiomatic approach, establishing its fundamental properties and relation to spacetime structure.

Findings

Sigma is traceless and invariant under electric-magnetic reciprocity.

Sigma is symmetric with 9 independent components when using Maxwell-Lorentz relations.

The framework completes the axiomatic foundation of pre-metric electrodynamics.

Abstract

We complete a metric-free axiomatic framework for electrodynamics by introducing the appropriate energy-momentum current Sigma of the electromagnetic field. We start from the Lorentz force density and motivate the form of Sigma. Then we postulate it (fourth axiom) and discuss its properties. In particular, it is found that Sigma is traceless and invariant under an electric-magnetic reciprocity transformation. By using the Maxwell-Lorentz spacetime relation (fifth axiom), Sigma is also shown to be symmetric, that is, it has 9 independent components