  Starting from nonequilibrium quantum field theory on a closed time path, we
derive kinetic equations for the strong-field regime of quantum electrodynamics
(QED) using a systematic expansion in the gauge coupling $e$. The strong field
regime is characterized by a large photon field of order $\mathcal{O}(1/e)$,
which is relevant for the description of, e.g., intense laser fields, the
initial stages of off-central heavy ion collisions, and condensed matter
systems with net fermion number. The strong field enters the dynamical
equations via both quantum Vlasov- and collision terms, which we derive to
order $\mathcal{O}(e^2)$. The strong-field scattering kernel couples the
transport equations to an equation for the fermion spectral function. The
description includes single photon emission, electron-positron pair
photoproduction, vacuum (Schwinger) pair production, their inverse processes,
medium effects and contributions from the field, which are not restricted to
the so-called locally-constant crossed field approximation. This extends known
kinetic equations commonly used in strong-field QED of intense laser fields. In
particular, we propose an expression for an asymptotic fermion pair number that
remains valid for strongly inhomogeneous fields. For the purpose of
analytically highlighting limiting cases, we also consider plane-wave fields. A
plane-wave particle picture is identified and it is shown how to recover
Furry-picture scattering amplitudes by further assuming negligible occupations.
Known on-shell descriptions are recovered for the case of simply peaked
ultrarelativistic fermion occupations. Collisional strong-field equations are
necessary to describe the dynamics to thermal equilibrium starting from
strong-field initial conditions.
