Nonperturbative infrared dynamics of three-dimensional QED with a four-fermion interaction - art. no. 045025

A nonlinear Schwinger-Dyson (SD) equation for the gauge boson propagator of massless QED in one time and two spatial dimensions is studied. It is show n that the nonperturbative solution leads to a nontrivial renormalization-g roup infrared fixed pr,int quantitatively close to the one found in the lea ding order of the 1/N expansion, with N the number of fermion flavors. In t he gauged Nambu-Jona-Lasinio (GNJL) model an equation for the Yukawa vertex is solved in an approximation given by the one-photon exchange and an anal ytic expression is derived fur the propagator of the scalar fermion-antifer mion composites. Subsequently, the mass and width of the scalar composites near the phase transition line are calculated as functions of the four-ferm ion couplings g and flavor number N. The possible relevance of these result s for describing particle-hole excitations, in particular antiferromagnetic correlations, observed in the underdoped cuprates, is briefly discussed.