Field equations in functional form

Starting from the functional equations governing the Green function of a single nucleon moving in an external field with radiative corrections, as given by Schwinger, a formulation is developed which relates this Green function to that of a nucleon moving in an arbitrary external field, without radiative corrections. In the case of neutral scalar meson theory in which the recoil of the nucleon is neglected, the Green function is obtained in closed form. Mass and Green-function renormalizations are easily done completely, and the singularities of the solution investigated, proving to be an interesting illustration of the expected behaviour in more realistic cases.