Resummation of QED radiative corrections in a strong constant crossed field

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 $g=\alpha {\chi }^{2/3}$, where the dynamical quantum parameter $\chi =e\sqrt{-(Fp{)}^2}/m^3$ combines the particle momentum $p$ with the external field strength tensor $F$. Here we present and discuss the first non-perturbative 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 $g\gg 1$. Whereas the breakdown of perturbation theory occurs already for $g\gtrsim 1$, the leading-order result remains dominant until the asymptotic regime $g\gg 1$ 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.

18 pages, 8 figures, 2 tables. A deep revision was made: Sections III A and Section V are completely rewritten [in particular, by including the new Eqs. (28), (56), (57) and Table II]; Figure 3 is modified; the Appendix is extended with new Eqs. (A.1), (A.10), (A.11) and Figure 8; new references are added, a lot of other small improvements are implemented