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It was shown recently that unambiguous description of electromagneticenvironments requires electromagnetic potentials; knowledge only of electricand magnetic fields is insufficient and can lead to error. Consequences of thatdemonstration are here applied to propagating fields, such as laser fields.Gauge invariance is replaced by symmetry preservation. This alteration makes itpossible to understand how the known failure of the convergence of perturbationexpansions in quantum electrodynamics (QED) follows from the fact that QED isincomplete; it does not contain its strong-field limit. Inherent in thatdemonstration are the strong-field coupling constant and the strong-fieldalteration of the mass shell of a charged particle. A variety of physicallyimportant consequences ensue, including the loss of guidance from Feynmandiagrams. The meaning of tests for the precision of QED is questioned sincesuch evaluations apply only to perturbative QED, but not to extensions requiredfor complete QED.

Fundamental formulation of electrodynamics revisited, and the precision of quantum electrodynamics