Mass singularity and confining property in QED 3

Abstract We discuss the properties of the position space fermion propagator in three dimensional QED which we found previouly based on Ward-Takahashi-identity for soft-photon emission vertex and spectral representation.There is a new type of mass singularity which governs the long distance behaviour.It leads the propagator vanish at large distance.This term corresponds to dynamical mass in position space.Our model shows confining property and dynamical mass generation for arbitrary coupling constant.Since we used dispersion retation in deriving spectral function there is a physical mass which sets a mass scale.For finite cut off the propagator dumps more slowly than the results of Dyson-Schwinger equation with bare vertex at high energy. Low energy behaviour of the proagator is modified to decrease by position dependent mass.In the limit of zero infrared cut-off the propagator vanishes with a new kind of infrared behaviour.