  Three equivalent methods allow to compute the antipode of the Hopf algebras
of Feynman diagrams in perturbative quantum field theory (QFT): the Dyson-Salam
formula, the Bogoliubov formula, and the Zimmermann forest formula. Whereas the
first two hold generally for arbitrary connected graded Hopf algebras, the
third one requires extra structure properties of the underlying Hopf algebra
but has the nice property to reduce drastically the number of terms in the
expression of the antipode (it is optimal in that sense).The present article is
concerned with the forest formula: we show that it generalizes to arbitrary
right-handed polynomial Hopf algebras. These Hopf algebras are dual to the
enveloping algebras of preLie algebras -a structure common to many
combinatorial Hopf algebras which is carried in particular by the Hopf algebras
of Feynman diagrams.
