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Fermion Spectrum at Ultrasoft Region in a Hot QED/QCD Plasma

An spectrum of an electron (quark) with ultrasoft momentum (p g^2T) is discussed at extremely high temperature in quantum electrodynamics (chromodynamics) with a resummed perturbation theory. We establish the existence of the pole suggested in the previous work of the electron (quark) propagator at ultrasoft region, and find that its pole position is p_0=\mp |p|/3-iζ, where ζis the damping rate which is of order g^2T ln 1/g, and the expression of its residue. We also discuss whether the resummation scheme preserves the gauge symmetry.