  The standard approximations of the Dyson--Schwinger equation lead to complex
singularities of the fermion propagator. In three-dimensional QED one can show
that this phenomenon might be related to confinement: a confining potential
leads to mass-like singularities at complex momenta, and thus to the absence of
a mass singularity on the real timelike axis. The correct treatment of the
vacuum polarization is essential for the confining nature of QED3.
