Generally Covariant Maxwell Theory for Media with a Local Response: Progress since 2000

TL;DR

This paper reviews the development of generally covariant Maxwell equations for media with local responses since 2000, highlighting its theoretical importance and applications in understanding electrodynamics in complex media.

Contribution

It compiles recent advances in formulating Maxwell's equations in a covariant manner for media with local responses, emphasizing progress since 2000.

Findings

Enhanced understanding of covariant Maxwell equations in media

Application to complex media with local responses

Framework for future theoretical developments

Abstract

In the recent decades, it became more and more popular for engineers, physicists, and mathematicians alike to put the Maxwell equations into a generally covariant form. This is particularly useful for understanding the fundamental structure of electrodynamics (conservation of electric charge and magnetic flux). Moreover, it is ideally suited for applying it to media with local (and mainly linear) response behavior. We try to collect the new knowledge that grew out of this development. We would like to ask the participants of EMTS 2016 to inform us of work that we may have overlooked in our review.