Breakdown of perturbative strong-field QED

4 problems

• All-order high-$\chi$ behavior of electron self-energy in a constant crossed field

  Partially resolved

  Theory says each extra layer of quantum correction grows with field strength as $\alpha$ times $\chi^{2/3}$, where $\chi$ measures the field the electron feels in its own frame. The question is what the sum of all layers gives once that combination reaches 1.

• Does the Ritus-Narozhny scaling survive in realistic finite-duration fields?

  Contested

  The predicted breakdown was derived for an idealized field that never switches off, while real laser pulses last a finite time. Calculations for finite pulses find much milder growth of the corrections, so it is unclear whether any real field shows the breakdown.

• What theory describes QED at $\alpha \chi^{2/3}$ much larger than one?

  Open

  If the step-by-step expansion fails, a different way of calculating is needed. The question is what electrons and photons actually do in that regime and what experiments would see.

• Can an experiment reach $\alpha \chi^{2/3}$ above one before radiation losses?

  Open

  To test the breakdown, an electron must feel a field about a thousand times the critical field in its own frame, but it loses energy to radiation while entering the field. The question is whether any machine can get electrons there intact.