Ultrasoft fermion mode and off-diagonal Boltzmann equation in quark-gluon plasma at high temperature

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We derive the generalized Boltzmann equation (GBE) near equilibrium from the Kadanoff-Baym equation for quark excitation with ultrasoft momentum (g²T, g: coupling constant, T: temperature) in quantum chromodynamics (QCD) at extremely high T, and show that the equation is equivalent to the self-consistent equation derived in the resummed perturbation scheme used to analyze the quark propagator. We obtain the expressions of the dispersion relation, the damping rate, and the strength of a quark excitation with ultrasoft momentum by solving the GBE. We also show that the GBE enables us to obtain the equation determining the n-point function containing a pair of quarks and (n-2) gluon external lines whose momenta are ultrasoft.