  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 the description of
a trion as an electron interacting with an exciton, we can obtain the trion
absorption through far simpler diagrams, written with electrons and
\emph{excitons}. These diagrams are quite novel because, for excitons being not
exact bosons, we cannot use standard procedures designed to deal with
interacting true fermions or true bosons. A new many-body formalism is
necessary to establish the validity of these electron-exciton diagrams and to
derive their specific rules. It relies on the ``commutation technique'' we
recently developed to treat interacting close-to-bosons. This technique
generates a scattering associated to direct Coulomb processes between electrons
and excitons and a dimensionless ``scattering'' associated to electron exchange
inside the electron-exciton pairs -- this ``scattering'' being the original
part of our many-body theory. It turns out that, although exchange is crucial
to differentiate singlet from triplet trions, this ``scattering'' enters the
absorption explicitly when the photocreated electron and the initial electron
have the same spin -- \emph{i}. \emph{e}., when triplet trions are the only
ones created -- \emph{but not} when the two spins are different, although
triplet trions are also created in this case. The physical reason for this
rather surprising result will be given.
