ar X iv : h ep - t h / 03 04 02 1 v 1 2 A pr 2 00 3 Low - Energy - Theorem Approach to one - particle singularity in QED 2 + 1 Yuichi Hoshino

Yuichi Hoshino Kushiro National College of Technology, Otanoshike nishi 2-32-1,Kushiro, Hokkaido 084,Japan Abstract 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 convergent but non-analytic fashion of the spectral function in momentum space.There seems to be a singularity associated with effective mass which is a sum of bare mass and a kind of radiative correction.Term by term integral converges and they have a logarithmic singularity associated with bare mass in perturbation theory.Weak coupling limit correctly reproduces a free field behaviour.