  We present a detailed analysis of the self-consistent system of kinetic
equations (KEs) describing electron-positron pair production from vacuum under
the action of a spatially homogeneous time-dependent electric field of
arbitrary polarization. The physical significance of all the basic functions of
the kinetic theory is ascertained. It is demonstrated that the total system of
the KEs consists of two coupled quasiparticle and spin subsystems with their
integrals of motion. A projection method is proposed in order to obtain the KE
system in two particular cases: linearly polarized external electric field and
(2+1)-dimensional description of quasiparticles in graphene. We also address
the energy conservation law taking into account the internal plasma field and
describe an alternative rigorous derivation of the KE system.
