Large orders in strong-field QED

TL;DR

This paper investigates large-order expansions in strong-field QED, revealing how vacuum birefringence and pair production emerge at high energies and intensities through nonperturbative analysis of the photon polarization tensor.

Contribution

It introduces a nonperturbative approach to analyze high-order expansions in strong-field QED using the photon polarization tensor and computer algebra.

Findings

Indices of refraction increase with frequency, indicating normal dispersion.

Factorial growth of expansion coefficients suggests nonperturbative effects like absorption.

Absorption and anomalous dispersion occur at high frequencies and field intensities.

Abstract

We address the issue of large-order expansions in strong-field QED. Our approach is based on the one-loop effective action encoded in the associated photon polarisation tensor. We concentrate on the simple case of crossed fields aiming at possible applications of high-power lasers to measure vacuum birefringence. A simple next-to-leading order derivative expansion reveals that the indices of refraction increase with frequency. This signals normal dispersion in the small-frequency regime where the derivative expansion makes sense. To gain information beyond that regime we determine the factorial growth of the derivative expansion coefficients evaluating the first 80 orders by means of computer algebra. From this we can infer a nonperturbative imaginary part for the indices of refraction indicating absorption (pair production) as soon as energy and intensity become (super)critical. These results compare favourably with an analytic evaluation of the polarisation tensor asymptotics. Kramers-Kronig relations finally allow for a nonperturbative definition of the real parts as well and show that absorption goes hand in hand with anomalous dispersion for sufficiently large frequencies and fields.