The trion: two electrons plus one hole versus one electron plus one exciton

We first show that, for problems dealing with trions, it is totally hopeless to use the standard many-body description in terms of electrons and holes and its associated Feynman diagrams. We then show how, by using a description as electrons interacting with excitons, we can obtain the trion absorption through far simpler electron-exciton diagrams. These diagrams are indeed novel because, for excitons being not exact bosons, standard procedures designed to deal with interacting true fermions or true bosons cannot be used. A new many-body formalism is in fact necessary to establish the validity of these electron-exciton diagrams. It relies on the "commutation technique" we recently developed to treat interaction with composite bosons. This technique generates a scattering associated to Coulomb processes between electrons and excitons, without electron exchange, and a "scattering" associated to electron exchange inside the electron-exciton pairs, without Coulomb process - this Pauli scattering being the original part of our new many-body theory.