  A basic concept to calculate physical features of non-ideal plasmas, such as
optical properties, is the spectral function which is linked to the
self-energy. We calculate the spectral function for a non-relativistic hydrogen
plasma in $GW$-approximation. In order to go beyond $GW$ approximation, we
include self-energy and vertex correction to the polarization function in
lowest order. Partial compensation is observed. The relation of our approach to
$GW$ and $GW\Gamma$ calculations in other fields, such as the band-structure
calculations in semiconductor physics, is discussed. From the spectral function
we derive the absorption coefficient due to inverse bremsstrahlung via the
polarization function. As a result, a significant reduction of the absorption
as compared to the Bethe-Heitler formula for bremsstrahlung is obtained.
