Abstract
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 Δμv by retaining only the μ=ν=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 (Σ(T)) are presented, for a range ofN values and for different approximate self-energies. The ratior=2Σ(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 ∏ L and ∏ T . It is concluded that a valuer=6 is a reasonable estimate in this model.
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