Coulomb Interaction in Atomically Thin Semiconductors and Density-Independent Exciton-Scattering Processes

In quantum-kinetic approaches to the dynamics of Coulomb-bound many-body correlations such as excitons, trions, biexcitons or higher-order correlations, a detailed knowledge of the many-body Coulomb Hamiltonian serving as a starting point is important. In this manuscript, the second-quantized description of the Coulomb interaction between Bloch electrons in a Heisenberg-equation-of-motion approach in atomically thin semiconductors is derived and reviewed. Emphasis is put on a discussion of Umklapp processes and the dielectric screening including all local-field effects. A link between \textit{ab initio} methods of screening and few-band models in effective-mass approximations for the quantum kinetics is established and all important Coulomb scattering processes contributing to the exciton energy landscape and density-independent exciton scattering are discussed.