An exact representation of the causal QED fermion Greens 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 Greens function in the simple case of a constant external field. Schwingers famous exact result is obtained as the limit as the order of the approximation approaches infinity.
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