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The Schwinger-Dyson equation for the massless fermion propagator in quenched four-dimensional QED is solved for different forms of the fermion-photon vertex. A nonperturbative, analytic solution that is multiplicatively renormalizable and self-consistently related to the vertex by the Ward identity is obtained. Its behavior is quantitatively different from that found in the simple ladder approximation, for instance.
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Curtis et al. (1991) studied this question.
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