Improving Euler-Heisenberg-Schwinger Effective Action with Dressed Photons

We implement a longstanding proposal by Weisskopf to apply virtual polarization corrections to
the in/out external fields in study of the Euler-Heisenberg-Schwinger effective action. Our approach
requires distinguishing the electromagnetic and polarization fields based on mathematical tools
developed by Bia lynicki-Birula, originally for the Born-Infeld action. Our solution is expressed
as a differential equation where the one-loop effective action serves as input. As a first result of
our approach, we recover the higher-order one-cut reducible loop diagrams discovered by Gies and
Karbstein.