Nonperturbative dispersive sector in strong (quasi-)Abelian fields

TL;DR

This paper explores the nonperturbative dispersive sector in strong (quasi-)Abelian fields, analyzing the separation of perturbative and nonperturbative contributions to the effective Lagrangian and energy density, with numerical and analytical methods.

Contribution

It introduces a method to distinguish perturbative and nonperturbative parts of the effective Lagrangian in strong fields and investigates their relative magnitudes.

Findings

Nonperturbative contributions can dominate perturbative ones.

Numerical analysis shows nonperturbative effects are significant across field strengths.

Modified Borel-Pade used to continue perturbative results into nonperturbative sector.

Abstract

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.