Field intensity and relativistic considerations in the choice of gauge in electrodynamics

Abstract

The properties of the electric field gauge are compared with the radiation gauge and other simple gauges for problems where intense-field and/or relativistic effects are significant. Electromagnetic shifts in free-electron mass and momentum, which can be of major importance in both kinematics and dynamics when the field is intense, and which are clearly in evidence in second-order radiation-gauge formulations, do not appear in the electric field gauge in any finite order of perturbation theory. Intense-field expressions like the closed-form Volkov solution, and mass and momentum intensity parameters, are shown to be invariant in form in simple gauges, but find no natural expression in the electric field gauge. It is also shown that intensity effects introduce strongly spin-coupled terms even in nonrelativistic problems. For both charged and neutral bound-state systems, crossed vector-potential terms occur in electric field gauge which prevent separation of the Schr\odinger equation into center-of-mass and relative-coordinate equations when the field intensity is high. This difficulty does not arise in the radiation gauge. These considerations inhibit the use of electric field gauge in intense-field problems.