Constraint on the QED Vertex from the Mass Anomalous Dimension $\gamma_m = 1$

Abstract

We discuss the structure of the non-perturbative fermion-boson vertex in quenched QED. We show that it is possible to construct a vertex which not only ensures that the fermion propagator is multiplicatively renormalizable, obeys the appropriate Ward-Takahashi identity, reproduces perturbation theory for weak couplings and guarantees that the critical coupling at which the mass is dynamically generated is gauge independent but also makes sure that the value for the anomalous dimension for the mass function is strictly 1, as Holdom and Mahanta have proposed.