  Strong background fields require a non-perturbative treatment, which is
afforded in QED by the Furry expansion of scattering amplitudes. It has been
conjectured that this expansion breaks down for sufficiently strong fields,
based on the asymptotic growth of loop corrections with increasing "quantum
nonlinearity", essentially the product of field strength and particle energy.
However, calculations to date have assumed that the background is constant. We
show here, using general plane waves of finite duration, that observables at
high quantum nonlinearity scale differently depending on whether intensity or
energy is large. We find that, at high energy, loop contributions to
observables tend to fall with increasing quantum nonlinearity, rather than
grow.
