The exciton many-body theory extended to arbitrary composite bosons

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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, 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, 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.