  The G\"oppert-Mayer (GM) gauge transformation, of central importance in
atomic, molecular, and optical physics since it connects the length gauge and
the velocity gauge, becomes unphysical as the field frequency declines towards
zero. This is not consequential for theories of transverse fields, but it is
the underlying reason for the failure of gauge invariance in the
dipole-approximation version of the Strong-Field Approximation (SFA). This
failure of the GM gauge transformation explains why the length gauge is
preferred in analytical approximation methods for fields that possess a
constant electric field as a zero-frequency limit.
