Comment on "All-Loop Result for the Strong Magnetic Field Limit of the Heisenberg-Euler Effective Lagrangian"

TL;DR

This paper critically examines a recent claim about the Euler-Heisenberg effective Lagrangian, revealing discrepancies with established series at the two-loop level, thus questioning the previous results' accuracy.

Contribution

It provides a second analysis of the all-loop results for the strong magnetic field limit, highlighting differences from prior claims at the two-loop order.

Findings

Discrepancies with the claimed all-loop results at two-loop level

Differences observed compared to the Schwinger-Dyson series

Questions raised about the accuracy of recent improvements

Abstract

We offer a 2nd look at the recently claimed improvement of Euler-Heisenberg-Schwinger (EHS) action [PRL \textbf{122} (2019) no.21, 211602 and post-publication correction]: We demonstrate a difference to the claimed concordance with the Schwinger-Dyson series starting at the two-loop level.