Abstract
As a toy model of quantum chromodynamics (QCD), we investigate the influence of the vacuum polarization on the photon propagator, in massless quantum electrodynamics in 2+1 dimensions (QED3), using the coupled Dyson–Schwinger equations for the fermion and photon propagators with a range of fermion–photon vertices. It is found that the form of the photon propagators in the Nambu–Goldstone and Wigner phases exhibit distinctly different behaviors and it is expected that similar things happen in QCD. Hence in the phenomenological application of QCD one should choose different forms of gluon propagator as input to solve the quark self-energy functions in the two different phases, especially in the study of QCD phase transitions. In addition, employing these results, we discuss the causation of dynamical chiral symmetry breaking (DCSB) in QED3 and compare it with that in QCD.
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