Analytical properties of the photon propagator and confinement in QED3

Abstract

Analytical properties of the photon propagator in QED3 in the N^1-approximation are considered. It is noticed that in given approximation if the dynamical fermions mass is nonzero this propagator has a single pole at the point k^2=0 and a branch point at k^2=-4m^2 (m is the fermion mass). When m=0, the propagator gets the pole at the spacelike domain of the variable k^2. It witnesses the unstability of the state conforming to the photon and leads to the screening of the source field at r speeds to infinity. The approximation by the rational function of the photon propagator containing the vacuum loops with massive fermions proposed by Gusynin, Hams and Reenders is shown to lead to the pole and the branch point at k^2=0 and to the pole in the spacelike domain as well. The arguments in favour of the statement that the presence of the dynamical fermions mass leads in QED3 to the confinement irrespectively of any approximation, are given.