Light-cone regular vertex in three-dimensional quenched QED

We study a model Schwinger-Dyson equation in three dimensions based on three-dimensional QED in the confining quenched approximation. We employ an ansatz for the dressed photon-fermion vertex function that does not have a singularity on the light cone. Our ansatz also allows us to study the relationship between the transverse part of the vertex and gauge independence of 〈ψψ〉. We find that the transverse part of the vertex is crucial to obtaining 〈ψψ〉 independent of the gauge parameter. It modifies both the infrared and ultraviolet behavior of the fermion propagator without upsetting the 1p² behavior expected of the mass function at large spacelike p².