Highly Radiating Charged Particles in a Strong Electromagnetic Field

TL;DR

This paper calculates the leading term of the electron mass operator in a strong electromagnetic field at high energies, using a non-perturbative QED approach, addressing longstanding theoretical controversies.

Contribution

It provides a non-perturbative calculation of the electron mass operator in ultra-strong fields, advancing understanding beyond traditional perturbative methods.

Findings

Derived the leading term of the electron mass operator at high energies in strong fields.

Extended calculations to the photon polarization operator in similar conditions.

Resolved longstanding theoretical controversies in high-field QED.

Abstract

We consider highly radiating ultra-relativistic electrons in a strong external electromagnetic field. High intensity radiative losses and consequent $e^+e^-$-pair production, appearing in the frame of quantum electrodynamics, determine indirectly mass operator of electrons in the strong field. We calculate a leading term of the mass operator at asymptotically high energies of electrons in a strong constant field. We do not use any perturbation theory based on a low ratio of this mass operator to the electron mass $m_e$, but only the original small parameter of quantum electrodynamics, the fine structure constant, $\alpha$. The analogous %but less nontrivial result is obtained for the polarization operator for photon propagator. These results resolve at least partially a very long-lasted controversy originating from traditional and straightforward application of perturbative approaches for description of highly radiating ultra-relativistic charged particles in a very strong electromagnetic fields.