Abstract
We investigate the behavior of the vacuum polarization ofthe gauge-boson Π and the wave-function renormalizationfactor of the fermion A in QED3, using the coupledDyson–Schwinger equations for the gauge-boson and fermionpropagator. Using several different ansätze for thefermion-gauge-boson vertex, we find that the wave-functionrenormalization factor A and especially the vacuum polarizationΠ have different behaviors in the dynamical chiral symmetrybreaking phase and in the chiral symmetric phase and hence inthe phenomenological applications of QED3 one should choosedifferent forms of gauge-boson propagator for these two phases.We also find that when adopting a specific ansätze of thefermion-gauge-boson vertex (ansätze (3)) the vacuum polarizationfunction equals its one-loop perturbative result in the chiralsymmetric phase. This fact suggests that in QED3 the Wigner vacuumcorresponds to the perturbative vacuum.
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