Fermion propagator in an out of equilibrium quantum-field system and the Boltzmann equation

We aim to construct from first principles a perturbative framework for studying nonequilibrium quantum-field systems that include massless Dirac fermions. The system of our concern is a quasiuniform system near equilibrium or a nonequilibrium quasistationary system. We employ the closed-time-path formalism and use the so-called gradient approximation. Essentially no further approximation is introduced. We construct a fermion propagator, with which a well-defined perturbative framework is formulated. In the course of the construction of the framework, we obtain the generalized Boltzmann equation that describes the evolution of the number-density functions of (anti)fermionic quasiparticles