Doubled Conformal Compactification

TL;DR

The paper demonstrates that standard conformal compactification of Minkowski spacetime causes discontinuities in electrodynamics at the light cone, and introduces a doubled conformal compactification to achieve a globally well-defined electromagnetic theory.

Contribution

It introduces the concept of doubled conformal compactification, resolving discontinuities in electrodynamics on the traditional conformal boundary.

Findings

Discontinuities in electrodynamics at the light cone are due to sign factors.

Doubled conformal compactification allows for globally well-defined electrodynamics.

Penrose diagrams illustrate the problem and its solution.

Abstract

We use Weyl transformations between the Minkowski spacetime and dS/AdS spacetime to show that one cannot well define the electrodynamics globally on the ordinary conformal compactification of the Minkowski spacetime (or dS/AdS spacetime), where the electromagnetic field has a sign factor (and thus is discountinuous) at the light cone. This problem is intuitively and clearly shown by the Penrose diagrams, from which one may find the remedy without too much difficulty. We use the Minkowski and dS spacetimes together to cover the compactified space, which in fact leads to the doubled conformal compactification. On this doubled conformal compactification, we obtain the globally well-defined electrodynamics.