Electromagnetic Geometry

TL;DR

This paper demonstrates a mapping of Maxwell's electromagnetism into Born-Infeld theory within a curved spacetime, suggesting that the dynamics and geometry of a theory can be viewed as different representations of the same physical system.

Contribution

It introduces a novel mapping between Maxwell's electromagnetism and Born-Infeld theory in a curved spacetime, encompassing all solutions of Maxwell's equations.

Findings

Maxwell's electromagnetism can be mapped into Born-Infeld theory in curved spacetime.

The mapping depends only on the electromagnetic field and is valid for all invariants.

This suggests dynamics and geometry choices are different representations of the same physics.

Abstract

We show that Maxwell's electromagnetism can be mapped into the Born-Infeld theory in a curved space-time, which depends only on the electromagnetic field in a specific way. This map is valid for any value of the two lorentz invariants $F$ and $G$ confirming that we have included all possible solutions of Maxwell's equations. Our result seems to show that specifying the dynamics and the space-time structure of a given theory can be viewed merely as a choice of representation to describe the physical system.