Structure of radiative corrections in a strong constant crossed field in the bubble-chain approximation

Abstract

We present a calculation of the electron mass operator combining the bubble-chain photon and the leading order electron propagators in a strong constant crossed electromagnetic field. The photon propagator is obtained by a summation of the Dyson series over 1PI polarization loop insertions and is accounted for in general form. By applying the derived mass operator, we find the bubble-chain electron propagator and the elastic scattering amplitude. The results are expressed in the general form of expansion over γ-matrix structures, each multiplied by a scalar invariant function of the electron virtuality and the quantum dynamical parameter χ. We perform their asymptotic analysis and identify the dominant contribution at χ 1. The presented calculations can be generalized by replacing the leading order electron propagator with the bubble-chain one.This will allow a consistent study the Dyson-Schwinger equations in the fully nonperturbative regime αχ 2/3 1 within the bubble-chain approximation. In addition, we accompany our paper with the open-access computer-algebraic scripts containing all the presented computations [https://github.com/ArsenyMironov/SFQED-Loops].

Particle-beam scattering from strong-field QED

“…It has been conjectured that loop corrections in the Furry expansion, in a CCF, scale at high field strength not with powers of α, but with powers of αχ 2/3 , in which χ is essentially the product of field strength and probe particle energy [68,69]. This has recently been confirmed for a class of electron self-energy diagrams to all loop orders [70] (and investigations continue into other loop corrections [71,72]).…”