  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{\l}ynicki-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.
