  We study the loop quantum cosmology of a flat
Friedmann-Lemaitre-Robertson-Walker space-time with a Maxwell field. We show
that many of the qualitative properties derived for the case of a massless
scalar field also hold for a Maxwell field. In particular, the big-bang
singularity is replaced by a quantum bounce, and the operator corresponding to
the matter energy density is bounded above by the same critical energy density.
We also numerically study the evolution of wave functions that are sharply
peaked in the low energy regime, and derive effective equations which very
closely approximate the full quantum dynamics of sharply peaked states at all
times, including the near-bounce epoch. In the process, the analytical and
numerical methods originally used to study the dynamics in LQC for the case of
a massless scalar field are substantially improved to handle the difficulties
(that generically arise for matter content other than a massless scalar field)
related to the presence of a Maxwell field.
