Impact of background field localization on vacuum polarization effects

TL;DR

This paper investigates how the localization of background electromagnetic fields influences nonlinear quantum vacuum effects like photon polarization and pair production, using analytical methods for Lorentzian-shaped inhomogeneities in QED.

Contribution

It provides a non-perturbative analysis of vacuum polarization effects in inhomogeneous fields with Lorentzian profiles, extending understanding beyond uniform field approximations.

Findings

Vacuum effects depend on the number of inhomogeneous directions (d).

Scaling laws for photon polarization flip are derived for different inhomogeneity dimensions.

Insights into pair production rates in localized background fields are obtained.

Abstract

We aim at insights about how localization of the background field impacts nonlinear quantum vacuum signatures probed by photons in purely magnetic, electric and crossed fields. The starting point of our study are the one-loop results for the Heisenberg-Euler effective Lagrangian and the photon polarization tensor in quantum electrodynamics (QED) evaluated in a uniform constant electromagnetic field. As is well known and often employed, especially in the weak-field limit, within certain restrictions these results also allow for the reliable analysis of vacuum polarization effects in slowly varying background fields. Here, our main interest is in manifestly non-perturbative effects. To this end, we make use of the fact that for the particular case of background field inhomogeneities of Lorentzian shape with $0\leq d\leq3$ inhomogeneous directions analytical insights are possible. We study the scaling of conventional nonlinear QED signatures, such as probe-photon polarization flip and probe-photon induced electron-positron pair production, with relevant parameters. Special attention is put on the $d$ dependence of the considered effects.