Low-energy-theorem approach to one-particle singularity in QED2+1 -: art. no. 075

We evaluate the spectral function of scalar and spinor propagator in three dimensional quantum electrodynamics with the use of Ward-Identity for soft-photon emission vertex. Exponentation of one-photon matrix element yields a full propagator in position space. It has asimple form as free propagator multiplied by quantum correction. But this is not an integrable function so that analysis in momentum space is not easy. Term by term integral converges and they have a logarithmic singularity associated with renormalized mass in perturbation theory. Renormalization constant vanishes for weak coupling,which suggests confinement of charged particle. There exsists a critical coupling constant below which bare mass vanishes and the vacuum expectation value of pair condensation is finite.