Excitons dressed by a sea of excitons

We here consider an exciton i embedded in a sea of N identical excitons 0. If the excitons are taken as true bosons, a bosonic enhancement factor N is found for i=0. If the exciton composite nature is kept, this enhancement not only exists for i=0, but also for any exciton having a center of mass momentum equal to the sea exciton momentum. This physically comes from the fact that an exciton with such a momentum can be transformed into a sea exciton by Pauli scattering, i.e., carrier exchange with the sea, making this exciton i not so much different from a sea exciton. This possible scattering, directly linked to the composite nature of the excitons, is irretrievably lost when the excitons are bosonized. The underlying interest of this work is in fact the calculation of the scalar products of N-exciton states, which turns out to be quite tricky, due to possible carrier exchanges between excitons. This work actually constitutes a crucial piece of our many-body theory for interacting composite bosons, because all physical effects involving composite bosons ultimately end by the calculation of such scalar products. The skeleton diagrams we here introduce to represent them, allow to visualize many-body effects linked to carrier exchanges in an easy way. They are conceptually different from Feynman diagrams, because of the special feature of the Pauli scatterings which originate from boson statistics departure.