Resummation of QED radiative corrections in a strong constant crossed field
A. A. Mironov, Sebastian Meuren, A. M. Fedotov
Abstract
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 $g=\ensuremath{\alpha}{\ensuremath{\chi}}^{2/3}$, where the dynamical quantum parameter $\ensuremath{\chi}=e\sqrt{\ensuremath{-}(Fp{)}^{2}}/{m}^{3}$ 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 $g\ensuremath{\gg}1$. Whereas the breakdown of perturbation theory occurs already for $g\ensuremath{\gtrsim}1$, the leading-order result remains dominant until the asymptotic regime $g\ensuremath{\gg}1$ 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.