Green's Function in Intense-Field Electrodynamics

The problem of an electron in the presence of an intense monochromatic electromagnetic field is studied from the standpoint of the exact Green's function for the electron in relativistic quantum mechanics. It is shown that the electron acquires a mass increment above the field-free mass. The Green's function is derived and investigated at some length. It is initially derived in a form which is very different from the free-electron Green's function. This form is shown to yield an interesting momentum relation for the electron, and to lead to a seeming level structure of the electron. The Green's function is then transformed to a different form in which the electromagnetic-field effects are manifest as corrections to the free-electron result. This form makes evident the field-strength and electron-momentum conditions which lead to significant quantitative deviations from the free-particle case. Most of the detailed discussion is devoted to the case of the scalar "electron," but results are also given for the spinor electron.