QED vacuum structure is receiving today renewed experimental interest. Here we consider super critical constant macroscopic magnetic fields on magnetars and vacuum birefringence induced by laboratory magnetic fields as probes of the QED vacuum response. Several new vacuum effects have been recognized beyond Euler-Heisenberg effective action. We study radiative corrections relevant to field strengths probed by astronomical sources. We supplement the well-known electron loop action with virtual excitations of particles typically studied outside the domain of the QED vacuum effects. We investigate further a suggestion made by Weisskopf in regard to self-consistency of the effective action computation and extend these considerations to the case of particle producing electric fields.
Virtual axion-like particle complement to Euler-Heisenberg-Schwinger action, Stefan Evans, Johann Rafelski Phys.Lett. B791 (2019) 331-334
Vacuum stabilized by anomalous magnetic moment, Stefan Evans, Johann Rafelski Phys.Rev. D98 (2018) no.1, 016006