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 ansätze 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 ansätze of the fermion-gauge-boson vertex (ansätze (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.