  As a toy model for QED in strong background fields, we consider the impact of
back-reaction and loop effects on scattering processes in quantum optics. We
show that neglecting back-reaction misses qualitative and quantitative features
of strong-field physics. We are able to study an analogue of the Narozhny-Ritus
conjecture on the scaling of higher loop diagrams with intensity: we prove that
there is no corresponding behaviour in our model. Implications for QED are
identified and discussed.
