  For half a century, Feynman diagrams have provided an enlightening way of
representing many-body effects between elementary fermions and bosons. They
however are quite inappropriate to visualize fermion exchanges taking place
between a large number of composite quantum particles. We propose to replace
them by "Shiva diagrams" for cobosons made of two fermions and by Shiva-like
and "Kali diagrams" for cofermions made of three fermions. We also show how
these fermion exchanges formally appear in a many-body theory appropriate to
composite quantum particles. This theory relies on an operator algebra based on
commutators and anticommutators, the usual scalar algebra based on Green
functions being valid for elementary bosons or fermions having strict
commutation relations, only.
