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Abstract

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 kinetic equations feature generalized scattering
amplitudes that have their own equation of motion in terms of 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 derive an
expression for the asymptotic fermion pair number that includes leading-order
collisions and remains valid for strongly inhomogeneous fields. For the purpose
of analytically highlighting limiting cases, we also consider plane-wave fields
for which it is shown how to recover Furry-picture scattering amplitudes by
further assuming negligible occupations. Known on-shell descriptions are
recovered in 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.