Beyond the instantaneous-exchange approximation for three-dimensional QED at finite temperature

Dynamical fermion mass generation is studied inN-flavour QED in three dimensions at finite temperature, using the Schwinger-Dyson (S-D) equation. Previous work (in the imaginary-time formalism) approximated the photon propagator ?µv by retaining only the µ=?=0 part, at zero frequency (“instantaneous exchange”). Here we calculate the photon propagator to leading order in 1/N, in the real-time formalism. Simple approximate forms for the longitudinal (?L) and transverse (?T) photon self-energies are proposed. The S-D equation is solved in both the instantaneous and retarded cases. Numerical results for the temperature dependence of the dynamically generated mass (S(T)) are presented, for a range ofN values and for different approximate self-energies. The ratior=2S(T=0)/kBTc is generally found to be somewhat reduced when retardation is included, and to depend quite sensitively on the low-momentum behaviour of ?L and ?T. It is concluded that a valuer=6 is a reasonable estimate in this model.