  In principle, calculation of a full Green's function in any field theory
requires knowledge of the infinite set of multi-point Green's functions, unless
one can find some way of truncating the corresponding Schwinger-Dyson
equations. For the fermion and boson propagators in QED this requires an {\it
ansatz} for the full three point vertex. Here we illustrate how the properties
of gauge invariance, gauge covariance and multiplicative renormalizability
impose severe constraints on this fermion-boson interaction, allowing a
consistent truncation of the propagator equations. We demonstrate how these
conditions imply that the 3-point vertex {\bf in the propagator equations} is
largely determined by the behaviour of the fermion propagator itself and not by
knowledge of the many higher point functions. We give an explicit form for the
fermion-photon vertex, which in the fermion and photon propagator fulfills
these constraints to all orders in leading logarithms for massless QED, and
accords with the weak coupling limit in perturbation theory at ${\cal
O}(\alpha)$. This provides the first attempt to deduce non-perturbative Feynman
rules for strong physics calculations of propagators in massless QED that
ensures a more consistent truncation of the 2-point Schwinger-Dyson equations.
The generalisation to next-to-leading order and masses will be described in a
longer publication.
