Behavior of Vacuum Polarization of Gauge-Boson and Wavefunction Renormalization Factor of Fermion in Different Phases of QED3

We investigate the behavior of the vacuum polarization of the gauge-boson Π and the wave-function renormalization factor of the fermion A in QED3, using the coupled Dyson-Schwinger equations for the gauge-boson and fermion propagator. Using several different ansaetze for the fermion-gauge-boson vertex, we find that the wave-function renormalization factor A and especially the vacuum polarization Π have different behaviors in the dynamical chiral symmetry breaking phase and in the chiral symmetric phase and hence in the phenomenological applications of QED3 one should choose different forms of gauge-boson propagator for these two phases. We also find that when adopting a specific ansaetze of the fermion-gauge-boson vertex (ansaetze (3)) the vacuum polarization function equals its one-loop perturbative result in the chiral symmetric phase. This fact suggests that in QED3 the Wigner vacuum corresponds to the perturbative vacuum.