  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.
