Effect of retardation on dynamical mass generation in two-dimensional QED at finite temperature

The effect of retardation on dynamical mass generation in QED in two space dimensions at finite temperature is studied, in the imaginary time formalism. The photon polarization tensor is evaluated to leading order in 1/N (where N is the number of flavours), and simple approximate closed form expressions are found for the fully retarded longitudinal and transverse propagators, which have the correct T → 0 limit. The resulting Schwinger-Dyson equation for the fermion mass (at order 1/N) has an infrared divergence associated with the contribution of the tranverse photon propagator; only the longitudinal contribution is retained, as in earlier treatments. For solutions in which the mass is a constant, it is found that retardation reduces the value of the parameter r (the ratio of twice the mass to the critical temperature) from about 10 to about 6, in agreement with a similar calculation in the real time formalism. The gap equation is then solved allowing the mass to depend on frequency (but not momentum), thus extending the study of retardation to the variable mass case for the first time.Solutions for T 6= 0 are obtained which join on smoothly to the correct T = 0 solution. It is found that there is a critical number of flavours, Nc,above which no mass is generated. The phase boundary in the N − T plane is calculated, and agrees qualitatively with that found in other variable mass (but non-retarded) calculations. The r value remains close to 6.Possibilities for including the transverse photon propagator are discussed.