BEYOND THE INSTANTANEOUS-EXCHANGE APPROXIMATION FOR 3-DIMENSIONAL QED AT FINITE-TEMPERATURE

Dynamical fermion mass generation is studied in N-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 Delta(mu v) by retaining only the mu=v=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 (Pi(L)) and transverse (Pi(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 (Sigma(T)) are presented, for a range of N values and for different approximate self-energies. The ratio r = 2 Sigma(T = 0)/k(B)T(c) is generally found to be somewhat reduced when retardation is included, and to depend quite sensitively on the low-momentum behaviour of Pi(L) and Pi(T). It is concluded that a value r = 6 is a reasonable estimate in this model.