The Influence of the Full Vertex and Vacuum Polarization on the Fermion Propagator in QED3

Abstract

We investigate the influence of the full vacuum polarization and vertex function on the fermion propagator, using the coupled Dyson--Schwinger equations for the photon and fermion propagator. We show that, within a range of vertex functions, the general behavior of the fermion propagator does not depend on the exact details of the vertex, both in the massless and in the massive phase. Independent of the precise vertex function, there is a critical number of fermion flavors for dynamical mass generation in $(2+1)$-dimensional QED. A consistent treatment of the vacuum polarization is essential for these results.