  Spin and hole excitation spectra and spectral weights are calculated for the
half-filled Hubbard model, as a function of $t/U$. We find that the high energy
spin spectra are sensitive to charge fluctuations. The energy difference
$\Delta(\pi,0)- \Delta(\pi/2,\pi/2)$, which is negative for the Heisenberg
model, changes sign at a fairly small $t/U\approx 0.053(5)$. The hole bandwidth
is proportional to $J$, and considerably larger than in the t-J models. It has
a minimum at ($\pi/2,\pi/2$) and a very weak dispersion along the
antiferromagnetic zone boundary. A good fit to the measured spin spectra in
La$_2$CuO$_4$ at $T=10K$ is obtained with the parameter values $U=3.1{\rm eV}$,
$t=0.35{\rm eV}$.
