Approximations to the QED fermion Green's function in a constant external field

An exact representation of the causal QED fermion Green's function, in an arbritrary external electromagnetic field, derived in Fried, Gabellini, and McKellar, and which naturally allows for nonperturbative approximations, is here used to calculate nonperturbative approximations to the Green's function in the simple case of a constant external field. Schwinger's famous exact result is obtained as the limit as the order of the approximation approaches infinity.