Analytic structure of the full fermion propagator in quenched and unquenched QED

We study the analytic structure of the electron propagator in the entire complex ${\mathit{p}}^2$ plane, using the Dyson-Schwinger equation. It is shown that in the usual ladder approximation there are two complex conjugate branch points, both in quenched and in unquenched strong coupling QED. There is, however, an essential difference between the quenched and the unquenched approximation: using the unquenched approximation, the branch points seem to approach the real axis in the continuum limit, in contrast with what happens in the quenched approximation.