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 by Fried, Gabellini and McKellar, and which naturally allows for non-perturbative approximations, is here used to calculate non-perturbative 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. 
S.K.J. Daniel and B.H.J. McKellar