  One of the central questions about the iron pnictides concerns the extent to
which their electrons are strongly correlated. Here we address this issue
through the phenomenology of the charge transport and dynamics, single-electron
excitation spectrum, and magnetic ordering and dynamics. We outline the
evidence that the parent compounds, while metallic, have electron interactions
that are sufficiently strong to produce incipient Mott physics. In other words,
in terms of the strength of electron correlations compared to the kinetic
energy, the iron pnictides are closer to intermediately-coupled systems lying
at the boundary between itinerancy and localization, such as V2O3 or Se-doped
NiS2, rather than to simple antiferromagnetic metals like Cr. This level of
electronic correlations produces a new small parameter for controlled
theoretical analyses, namely the fraction of the single-electron spectral
weight that lies in the coherent part of the excitation spectrum. Using this
expansion parameter, we construct the effective low-energy Hamiltonian and
discuss its implications for the magnetic order and magnetic quantum
criticality. Finally, this approach sharpens the notion of magnetic frustration
for such a metallic system, and brings about a multiband matrix t-J1-J2 model
for the carrier-doped iron pnictides.
