Derivation of the zeroth retardation order Boltzmann equation from nonstandard space-time Wigner quantum kinetics

摘要

A derivation of the equation of motion satisfied by a prototype of the forward space-time Wigner distribution, that incorporates a Fourier transformation of truncated time shifts as compared with the standard Wigner distribution, is carried out in the case of a many-body system within the formalism of nonequilibrium Green's functions of quantum field theory. In particular, the single-particle equation found in Lopez and Soler (2016) is recovered when the self-energy interaction effects are neglected. Then, a sinc-corrected quantum kinetic Boltzmann equation is derived that rules the evolution of the standard Wigner transform, which is shown to be reduced to the usual Boltzmann equation when only binary elastic collisions are considered. (C) 2019 Elsevier Ltd. All rights reserved.