  We show, in great detail, how the perturbative tools of quantum field theory
allow one to rigorously obtain: a ``categorified'' Faa di Bruno type formula
for multiple composition, an explicit formula for reversion and a proof of
Lagrange-Good inversion, all in the setting of multivariable power series. We
took great pains to offer a self-contained presentation that, we hope, will
provide any mathematician who wishes, an easy access to the wonderland of
quantum field theory.
