  We compute the self-energy for the half-filled Hubbard model on a square
lattice using lattice quantum Monte Carlo simulations and the dynamical vertex
approximation. The self-energy is strongly momentum dependent, but it can be
parametrized via the non-interacting energy-momentum dispersion
$\varepsilon_{\mathbf{k}}$, except for pseudogap features right at the Fermi
edge. That is, it can be written as $\Sigma(\varepsilon_{\mathbf{k}},\omega)$,
with two energy-like parameters ($\varepsilon$, $\omega$) instead of three
($k_x$, $k_y$ and $\omega$). The self-energy has two rather broad and weakly
dispersing high energy features and a sharp $\omega= \varepsilon_{\mathbf{k}}$
feature at high temperatures, which turns to $\omega=
-\varepsilon_{\mathbf{k}}$ at low temperatures. Altogether this yields a Z- and
reversed-Z-like structure, respectively, for the imaginary part of
$\Sigma(\varepsilon_{\mathbf{k}},\omega)$. We attribute the change of the low
energy structure to antiferromagnetic spin fluctuations.
