in question – preservation of the propagation property of a plane-wave field – is not often mentioned, even in the context of very strong fields where this symmetry is crucial [@hrup]. The demand for the preservation of the propagation property imposes a strong limitation on possible gauge transformations. In the presence of a simultaneous scalar interaction, like a Coulomb binding potential, only the radiation gauge is possible [@hrgge]. This limitation to a unique gauge exists in both classical and quantum domains. An important aspect of this problem is that the widely-used dipole approximation in the description of laser-caused effects suppresses this symmetry, thus masking the errors that follow from ignoring this basic property. Both the constant-electric-field and the propagating-field examples admit of only one possible gauge. This lack of gauge-equivalent alternatives is extremely important, since both situations represent commonplace physical environments. This is in contrast to the specialized Aharonov-Bohm effect.

An immediate consequence of the demonstrated fact that some nominally valid gauge transformations can have unphysical consequences is that a gauge transformation is not a unitary transformation. This is discussed in Section III, where it is shown to be related to the construction of exact transition amplitudes.

The impossibility of 