Constructing the fermion-boson vertex in three-dimensional QED - art. no. 105001

We derive perturbative constraints on the transverse part of the fermion-bo son vertex in massive three-dimensional QED through its one-loop evaluation in an arbitrary covariant gauge. Written in a particular form, these const raints naturally lead us to the first nonperturbative construction of the v ertex, which is in complete agreement with its one-loop expansion in all mo mentum regimes. Without affecting its one-loop perturbative properties, we also construct an effective vertex in such a way that the unknown functions defining it have no dependence on the angle between the incoming and outgo ing fermion momenta. Such a vertex should be useful for the numerical study of dynamical chiral symmetry breaking, leading to more reliable results.