Perturbative Out of Equilibrium Quantum Field Theory beyond the Gradient Approximation and Generalized Boltzmann Equation

Using the closed-time-path formalism, we construct perturbative frameworks,in terms of quasiparticle picture, for studying quasiuniform relativisticquantum field systems near equilibrium and non-equilibrium quasistationarysystems. We employ the derivative expansion and take in up to the second-orderterm, i.e., one-order higher than the gradient approximation. Afterconstructing self-energy resummed propagator, we formulated two kind ofmutually equivalent perturbative frameworks: The first one is formulated on thebasis of the ``bare'' number density function, and the second one is formulatedon the basis of ``physical'' number density function. In the course ofconstruction of the second framework, the generalized Boltzmann equationsdirectly come out, which describe the evolution of the system.Comment: LaTeX2e, 20 page