  We calculate the zero-temperature self-energy to fourth-order perturbation
theory in the Hubbard interaction $U$ for the half-filled Hubbard model in
infinite dimensions. For the Bethe lattice with bare bandwidth $W$, we compare
our perturbative results for the self-energy, the single-particle density of
states, and the momentum distribution to those from approximate analytical and
numerical studies of the model. Results for the density of states from
perturbation theory at $U/W=0.4$ agree very well with those from the Dynamical
Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with
the Dynamical Density-Matrix Renormalization Group. In contrast, our results
reveal the limited resolution of the Numerical Renormalization Group approach
in treating the Hubbard bands. The momentum distributions from all approximate
studies of the model are very similar in the regime where perturbation theory
is applicable, $U/W \le 0.6$. Iterated Perturbation Theory overestimates the
quasiparticle weight above such moderate interaction strengths.
