On the Pre-metric Formulation and Nonlinearization of Charge-free Electrodynamics

TL;DR

This paper develops a coordinate-free, pre-metric framework for charge-free Maxwell electrodynamics and introduces a nonlinear extension, providing formal results for static and dynamic cases and discussing the motivation for nonlinearization.

Contribution

It introduces a novel pre-metric nonlinear formulation of charge-free electrodynamics, extending existing linear theories with a formal, geometric approach.

Findings

Formal pre-metric nonlinear formulations for static and dynamic cases

Explicit mathematical relations for nonlinear extensions

Discussion on the motivation and potential of nonlinearization

Abstract

This paper presents a coordinate free pre-metric formulation of charge free Maxwell-Minkowski electrodynamics, and of the developed by the authors non-linear Extended Electrodynamics. First we introduce some formal relations from multilinear algebra and differential geometry to be used further. Then we recall and appropriately modify the existing pre-metric formulation of linear charge free electrodynamics in pre-relativistic and relativistic forms as preparation to turn to corresponding pre-metric nonlinearization. After some preliminary examples and notes on nonlinearization, we motivate our view for existence and explicit formulation of time stable subsystems of the physical field objects considered. Section 5 presents the formal results of our approach on the pre-metric nonlinear formulations in static case, in time-dependent case, and in space-time formulation. In the Conclusion we give our general view on "why and how to nonlinearize". The Appendix gives a possible formal extension of our aproach to many subsystem field objects.