Resummation of QED radiative corrections in a strong constant crossed field

By considering radiative corrections of up to 3rd-loop order, Ritus and Narozhny conjectured that the proper expansion parameter for QED in a strong constant crossed field is g=αχ2/3, where the dynamical quantum parameter χ=e-(Fp)2/m3 combines the particle momentum p with the external field strength tensor F. Here we present and discuss the first nonperturbative result in this context, the resummed bubble-type polarization corrections to the electron self-energy in a constant crossed field. Our analysis confirms the relevance of the scaling parameter g to the enhancement of bubble-type radiative corrections. This parameter actually represents the characteristic value of the ratio of the 1-loop polarization bubble to the photon virtuality. After an all-order resummation we identify and discuss two contributions to the self-energy with different formation regions and asymptotic behavior for g≫1. Whereas the breakdown of perturbation theory occurs already for g≳1, the leading-order result remains dominant until the asymptotic regime g≫1 is reached. However, the latter is specific to processes like elastic scattering or photon emission and does not have to remain true for general higher-order QED processes.