Nonperturbative dispersive sector in strong (quasi-)Abelian fields

In strong (quasi-)Abelian fields, even at the one-loop level of the couplin g constant, quantum fluctuations of fermions induce an effective Lagrangian density whose imaginary (absorptive) part is purely nonperturbative and kn own to be responsible for the fermion-antifermion pair creation. On the oth er hand, the induced real (dispersive) part has perturbative and nonperturb ative 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 numer ically that the nonperturbative contributions are in general comparable wit h or larger than the induced perturbative ones. We arrive at qualitatively similar conclusions also for the induced energy density. Further, we invest igate numerically the quasianalytic continuation of the perturbative result s into the nonperturbative sector, by employing (modified) Borel-Pade. It t urns out that in the case at hand, we have to integrate over renormalon sin gularities, but there is no renormalon ambiguity involved.