(2+1)-Dimensional QED with Dynamically Massive Fermions in the Vacuum Polarization

Abstract

We study chiral symmetry breaking in $\mathrm{QE}{\mathrm{D}}_3$ with $N_f$ flavors of four-component fermions. A closed system of Schwinger-Dyson equations for fermion and photon propagators and the full fermion-photon vertex is proposed, which is consistent with the Ward-Takahashi identity. A simplified version of that set of equations is reduced (in nonlocal gauge) to the equation for a dynamical fermion mass function, where the one-loop vacuum polarization with dynamically massive fermions has been taken into account. The linearized equation for the fermion mass function is analyzed in real space. The analytical solution is compared with the results of numerical calculations of the nonlinear integral equation in momentum space.

Comments: 17 pages, ReVTeX file and 3 uuencoded figures in one file