Off-diagonal kinetic theory in ultrasoft momentum region at high temperature

Abstract

We derive a linearized kinetic equation for fermionic excitations with an ultrasoft momentum, ${g}^{2}T$, from the Kadanoff-Baym equation in a Yukawa model and quantum electrodynamics (QED) at extremely high $T$, where $g$ is the coupling constant. We show that this equation is equivalent to the self-consistent equation in the resummed perturbation theory used in the analysis of the fermion spectrum with the ultrasoft momentum at the leading order. Furthermore, we derive the equation that determines the $n$-point function with external lines for a pair of fermions and ($n\ensuremath{-}2$) bosons with ultrasoft momenta in QED.