  The radiative corrections to Compton scattering vanish in the low-energy
limit in all orders of perturbation theory. This theorem, which is well-known
for Abelian gauge theories, is proved in the electroweak Standard Model.
Moreover, analogous theorems are derived for photon scattering off other
charged particles, in particular W bosons. Since the theorems follow from gauge
invariance and on-shell renormalization, their derivation is most conveniently
performed in the framework of the background-field method.
