  This paper concerns the kinetic limit of the Dirac equation with random
electromagnetic field. We give a detailed mathematical analysis of the
radiative transport limit for the phase space energy density of solutions to
the Dirac equation. Our derivation is based on a martingale method and a
perturbed test function expansion. This requires the electromagnetic field to
be a space-time random field.
  The main mathematical tool in the derivation of the kinetic limit is the
matrix-valued Wigner transform of the vector-valued Dirac solution. The major
novelty compared to the scalar (Schr\"odinger) case is the proof of convergence
of cross-modes to 0 weakly in space and almost surely in probability. The
propagating modes are shown to converge in an appropriate strong sense to their
deterministic limit.
