transformations (see, for example, the classic text by Jackson [@jackson]) is that the generating function must be a scalar function that satisfies the homogeneous wave equation, as in Eq. (\[c\]). This is satisfied by the function (\[u\]). The only other condition is the Lorenz condition (\[j\]), which is satisfied by the potentials before and after transformation. However, there is no condition that guarantees preservation of symmetries inherent in the physical problem. It is not enough to employ appropriate fields; it is necessary to employ the appropriate potentials to ensure that all aspects of the physical problem are rendered properly.

This writer is unaware of any instance where inappropriate potentials have been accepted and employed in this exceedingly simple problem. The same cannot be said for the next example.

Plane-wave field
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Laser fields are of central importance in contemporary physics, and laser fields are plane-wave fields. A plane-wave field is the only electromagnetic phenomenon that has the ability to propagate indefinitely in vacuum without the continued presence of sources. In the typical laboratory experiments with lasers, the practical consequence of this ability to propagate without need for sources means that all fields that arrive at a target can only be 