  We consider violation of Lorentz invariance in QED induced by a very high
frequency background wave. An effective theory is obtained by averaging
observables over the rapid field oscillations. This preserves Ward identities
and restores translation invariance below the high frequency scale, but only
partial Lorentz invariance: we show that the effective theory is C-invariant
SIM(2)-QED in Very Special Relativity. Averaging generates the nonlocal terms
familiar from SIM(2) theories, while the short-distance behaviour of the
background field fermion propagator generates the infinite number of
higher-order vertices of SIM(2)-QED.
