Fermions at high temperature

We calculate the self-energy of massless fermions interacting with massless bosons at high temperature by summing the set of ring diagrams. This leads to an effective one-loop equation. We further approximate the boson self-energy by a temperature-dependent mass squared which is of order (gT)2. At low momenta, p<g2T, the fermion dispersion relation is =(1/3p, whereas for high momenta, p>gT, it is =p. In the intermediate region, g2T<p<gT, the fermion oscillations are overdamped and do not propagate. We speculate that this may be due to spatial inhomogeneities caused by the formation of resonant or coherent states of bosons and fermions, which have a characteristic size of 1/gT and a characteristic separation of 1/g2T.