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Title: What theory describes QED at $\alpha \chi^{2/3}$ much larger than one
Plain: 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.
Precise: Assuming the loop expansion in a constant crossed field fails for $\alpha \chi^{2/3} >> 1$, construct a nonperturbative description, for example self-consistent Schwinger-Dyson equations for the dressed electron and photon propagators with a controlled truncation, an effective running coupling, or a semiclassical strong-coupling expansion. Give the resulting dressed dispersion relations and the rates of photon emission and pair creation, and show that the scheme reproduces the perturbative results for $\alpha \chi^{2/3} << 1$.
Settled by: A nonperturbative framework whose truncation error is controlled, verified against known one- and two-loop results, and yielding testable rates.
Kind: phenomenon
Answer type: mechanism
References: (empty)
Literature status: open
Status note: (empty)
Posed since: (empty)