  We review recent results on many-body effects in the luminescence from
semiconductor nanostructures. Many-body luminescence from highly excited
quantum-confined structures is conceptually important topic since a new
parameter, a level spacing, plays a crucial role. This spacing is not merely a
discretization of the bulk luminescence spectrum, as it could seem. The
interplay of finite spacing with interactions (even weak) results in a highly
nontrivial sequence of emission lines, their heights revealing the many-body
correlations in the system. Here the complex structure of the emission
spectrum, resulting from the shakeup processes in many-particle (but finite)
system, is demonstrated for a confined electron-hole system of a particular
geometry, in which the interacting carriers are confined to a ring. For this
geometry, the Luttinger liquid theory allows one to exactly calculate the
intensities of all many-body spectral lines. The positions of the lines are
governed by the relation of the level spacings for electrons and holes. While
close to the emission threshold the interactions cause only weak shakeup
satellites of the single-particle lines, away from the threshold the discrete
luminescence spectrum is completely dominated by the many-body transitions. We
describe the Luttinger liquid approach for calculations of optical spectra in
finite one-dimensional systems. The calculations are preceded by a detailed
review of experimental and theoretical work on many-body luminescence from
various infinite systems. We also review the current status of the experimental
and theoretical research on quantum nanorings.
