Mass-Shell Behavior of Electron Propagator at Low Temperature

In high temperature gauge theories the fermion propagator is quite di erent than at zero temperature [1] and calculations require the Braaten-Pisarski resummation of hard thermal loops [2{4]. One of the important quantities to be calculated is the imaginary part of the fermion selfenergy, or damping rate, which has been computed in various circumstances. In QCD the massless gluons are so changed by thermal e ects that a resummed gluon propagator is always necessary to compute thermal damping rates. Whether the quark masses are small or large compared to gT determines if a resummed quark propagator is required. The quark damping rate has been computed in both cases [2,5] and the potential infrared divergences are controlled by incorporating a magnetic screening mass. The absence of a magnetic screening mass in QED makes the electromagnetic damping rates more problematic [6]. It appears that at high temperature (eT m) the electron propagator at large time does not decay exponentially [7]. The same behavior is observed numerically in scalar QED [8]. In QED at low temperature (eT m) neither the electron nor photon propagator require Braaten-Pisarski resummation. One would expect very little qualitative di erence between low temperature and zero temperature. However, explicit calculation will show that there is an important di erence: at T = 0 the electron propagator has a branch cut at the mass shell but for T > 0 the propagator has a simple pole.