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In principle, calculation of a full Green's function in any field theoryrequires knowledge of the infinite set of multi-point Green's functions, unlessone can find some way of truncating the corresponding Schwinger-Dysonequations. For the fermion and boson propagators in QED this requires an {\itansatz} for the full three point vertex. Here we illustrate how the propertiesof gauge invariance, gauge covariance and multiplicative renormalizabilityimpose severe constraints on this fermion-boson interaction, allowing aconsistent truncation of the propagator equations. We demonstrate how theseconditions imply that the 3-point vertex {\bf in the propagator equations} islargely determined by the behaviour of the fermion propagator itself and not byknowledge of the many higher point functions. We give an explicit form for thefermion-photon vertex, which in the fermion and photon propagator fulfillsthese constraints to all orders in leading logarithms for massless QED, andaccords with the weak coupling limit in perturbation theory at ${\calO}(\alpha)$. This provides the first attempt to deduce non-perturbative Feynmanrules for strong physics calculations of propagators in massless QED thatensures a more consistent truncation of the 2-point Schwinger-Dyson equations.The generalisation to next-to-leading order and masses will be described in alonger publication.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Building the Full Fermion-Photon Vertex of QED by Imposing  Multiplicative Renormalizability of the Schwinger-Dyson Equations for the  Fermion and Photon Propagators