  In strong (quasi-)Abelian fields, even at the one-loop level of the coupling
constant, quantum fluctuations of fermions induce an effective Lagrangian
density whose imaginary (absorptive) part is purely nonperturbative and known
to be responsible for the fermion-antifermion pair creation. On the other hand,
the induced real (dispersive) part has perturbative and nonperturbative
contributions. In the one-loop case, we argue how to separate the two
contributions from each other for any strength of the field. We show
numerically that the nonperturbative contributions are in general comparable
with or larger than the induced perturbative ones. We arrive at qualitatively
similar conclusions also for the induced energy density. Further, we
investigate numerically the quasianalytic continuation of the perturbative
results into the nonperturbative sector, by employing (modified) Borel-Pade. It
turns out that in the case at hand, we have to integrate over renormalon
singularities, but there is no renormalon ambiguity involved.
