  A non-linear Schwinger-Dyson (SD) equation for the gauge boson propagator of
massless QED in one time and two spatial dimensions is studied. It is shown
that the nonperturbative solution leads to a nontrivial renormalization-group
infrared fixed point quantitatively close to the one found in the leading order
of the 1/N expansion, with N the number of fermion flavors. In the 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 analytic expression is
derived for the propagator of the scalar fermion-antifermion composites.
Subsequently, the mass and width of the scalar composites near the phase
transition line are calculated as functions of the four-fermion coupling g and
flavor number N. The possible relevance of these results for describing
particle-hole excitations, in particular antiferromagnetic correlations,
observed in the underdoped cuprates, is briefly discussed.
