significant, since it places the present work outside the scope of a Yang-Mills theory [@yangmills]. Quantum electrodynamics (QED) is a Yang-Mills theory, but standard QED does not incorporate strong-field theory. Strong-field theories contain an apparent intensity-dependent mass shift, discovered independently by Sengupta [@sengupta] and by the present author [@hrdiss; @hr62]. This mass shift can be explained in terms of a demand for covariance in external fields [@hrup]. The mass shift is a fundamental phenomenon in strong-field physics [@hrje], but it does not exist in the context of the quantized fields of QED [@hrdiss; @hr62; @jehr].

Section II below discusses two basic examples that exhibit pairs of potential choices that describe exactly the same fields, but where one set of potentials is physically acceptable and the other is not. One example is the simplest possible case: the classical interaction of a charged particle with a constant electric field. Of the two possibilities for gauge choice, one contradicts Noether’s Theorem [@noether]. There is no such problem with the alternative gauge. The next example is the interaction of a charged particle with a plane-wave field, such as the field of a laser. In this case, the key factor is that the symmetry principle 