  We address the question of the degree of spatial non-locality of the self
energy in the iron-based superconductors, a subject which is receiving
considerable attention. Using LiFeAs as a prototypical example, we extract the
self energy from angular-resolved photoemission spectroscopy (ARPES) data. We
use two distinct electronic structure references: density functional theory in
the local density approximation and linearized quasiparticle self consistent GW
(LQSGW). We find that with the LQSGW reference, spatially local dynamical
correlations provide a consistent description of the experimental data, and
account for some surprising aspects of the data such as the substantial out of
plan dispersion of the electron Fermi surface having dominant xz/yz character.
Hence, correlations effects can be separated into static non-local
contributions well described by LQSGW and dynamical local contributions. Hall
effect and resistivity data are shown to be consistent with this description.
