  We analyze the many-particle correlations that affect the optical properties
of two-dimensional semiconductors. These correlations manifest themselves
through the specific optical resonances such as excitons, trions, etc. Starting
from the generic electron-hole Hamiltonian and employing the microscopic
Heisenberg equation of motion the infinite hierarchy of differential equations
can be obtained. In order to decouple the system we address the cluster
expansion technique which provides a regular procedure of consistent accounting
of many-particle correlation contributions into the interband polarization
dynamics. In particular, the partially taken into account three-particle
correlations modify the behavior of absorption spectra with the emergence of a
trion-like peak additional to excitonic ones. In contrast to many other
approaches, the proposed one allows us to model the optical response of 2d
semiconductors in the regime when the Fermi energies are of the order of the
exciton and trion binding energies, thus allowing us to rigorously model the
onset of the excitonic Mott transition, the regime being recently studied in
various 2d semiconductors, such as transition metal dichalcogenides.
