  It was shown recently that unambiguous description of electromagnetic
environments requires electromagnetic potentials; knowledge only of electric
and magnetic fields is insufficient and can lead to error. Consequences of that
demonstration are here applied to propagating fields, such as laser fields.
Gauge invariance is replaced by symmetry preservation. This alteration makes it
possible to understand how the known failure of the convergence of perturbation
expansions in quantum electrodynamics (QED) follows from the fact that QED is
incomplete; it does not contain its strong-field limit. Inherent in that
demonstration are the strong-field coupling constant and the strong-field
alteration of the mass shell of a charged particle. A variety of physically
important consequences ensue, including the loss of guidance from Feynman
diagrams. The meaning of tests for the precision of QED is questioned since
such evaluations apply only to perturbative QED, but not to extensions required
for complete QED.
