Physical restrictions on the choice of electromagnetic gauge and their   practical consequences
  It is shown that electromagnetic potentials convey physical information beyond that supplied by electric and magnetic fields alone, and are thus more fundamental. Observable physical properties can impose conditions on the selection of electromagnetic gauge (i.e. sets of potentials) that are explicit and restrictive. This is true both classically and quantum mechanically. The implication that the choice of gauge carries physical information is confirmed by exhibiting a set of potentials that describes fields correctly, but that violates physical constraints. The basic conclusions are that physical requirements place limits on acceptable gauges; and that potentials are more fundamental than fields in both classical and quantum physics, representing a major generalization of the quantum-only Aharonov-Bohm effect. These important properties are obscured if the dipole approximation is employed. The properties demonstrated here relate directly to conditions that exist in strong-field laser applications. 
H. R. Reiss
quant-ph