ar X iv : h ep - t h / 05 10 03 6 v 6 1 2 O ct 2 00 5 Mass singularity and confinement in QED 3 Yuichi

To search the infrared behaviour of the propagator in three dimensional QED ordinary perturbative method is not appropriate because of its bad infrared divergences[4].Assuming spectral representation and LSZ reduction formula,we evaluate the infrared behaviour or the mass singularity of the fermion propagator in three dimensional QED as in four dimension.In quenched case with bare photon mass we obtain the Coulomb energy and Dynamical mass by lowest intermediate state.After exponentiation of this leads the non-perturbative propagator. Including massless vacuum polarization the short distance part of the propagator has a logarithmic correction.In the long distance Coulomb force is screened to suppress mass generation.Confining property and renormalization constants are discussed.