  The optical absorption of a many (continuum) polaron gas is derived in the
framework of a variational approach at zero temperature and weak or
intermediate electron-phonon coupling strength. We derive a compact formula for
the optical conductivity of the many-polaron system taking into account
many-body effects in the electron or hole system. Within the method presented
here, these effects are contained completely in the dynamical structure factor
of the electron or hole system. This allows to build on well-established
studies of the interacting electron gas. Based on this approach a novel feature
in the absorption spectrum of the many-polaron gas, related to the emission of
a plasmon together with a phonon, is identified. As an application and
illustration of the technique, we compare the theoretical many-polaron optical
absorption spectrum as derived in the present work with the `d-band' absorption
feature in Nd$_{2}$CuO$_{2}$. Similarities are shown between the theoretically
and the experimentally derived first frequency moment of the optical absorption
of a family of differently doped Nd$_{2-x}$Ce$_{x}$CuO$_{4-y}$ materials.
