The exciton many-body theory extended to arbitrary composite bosons

We have recently constructed a many-body theory for composite excitons, in which the possible carrier exchanges between $N$ excitons can be treated exactly through a set of dimensionless ``Pauli scatterings'' between two excitons. Many-body effects with excitons turn out to be rather simple because excitons are the exact one-electron-hole-pair eigenstates of the semiconductor Hamiltonian, thus forming a complete orthogonal set for one-pair states. It can however be of interest to extend this new many-body theory to more complicated composite bosons, \emph{i. e.}, ``cobosons'', which are not necessarily the one-pair eigenstates of the system Hamiltonian, nor even orthogonal. The purpose of this paper is to derive the ``Pauli scatterings'' and the ``interaction scatterings'' of these cobosons formally, \emph{i. e.}, just in terms of their wave functions and the interaction potentials which exist between the fermions from which they are constructed. We also explain how to derive many-body effects in this very general system of composite bosons.