Low-Energy Theorem Approach to One-Particle Singularity in QED{2+1}

Abstract

We evaluate the propagator of scalar and spinor in three dimensional quantum electrodynamics with the use of Ward-Identity for soft-photon emission vertex.We work well in position space to treat infrared divergences in our model. Exponentiation of one-photon matrix element yields a full propagator in position space.It has a simple form as free propagator multiplied by quantum correction.And it shows a new type of mass singularity.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 above which the vacuum expectation value of pair condensation is finite.