What Are the Hidden Predictions of QED in the Classical Limit?

[Albereo]

I recently read somewhere that the predictions of QED in the classical limit haven't been nearly as well-studied as, say, the classical limit of quantum mechanics.

This is a little confusing: doesn't QED just reduce to Maxwellian electrodynamics with additional small nonlinear quantum mechanical terms? If that's the case, it would seem that classical QED has been studied. Does the comment imply that Maxwell's equations with the nonlinear terms haven't been deeply investigated?

What else might remain of classical QED predictions to study?

 

[Bill_K]

What they probably mean by "QED in the classical limit" is more commonly called external field problems, in which the starting point is a classical electromagnetic field such as a Coulomb field, and radiative corrections to various processes are then calculated using QED. This includes things like the Lamb shift. Scattering of photons by a Coulomb field, etc. The claim that these things have not been well-studied of course is not true.