2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55909The recently discovered formalism underlying renormalization theory, the Hopf algebra of rooted trees, allows to generalize Chen's lemma. In its generalized form it describes the change of a scale in Green functions, and hence relates to the operator product expansion. Hand in hand with this generalization goes the generalization of the ordinary factorial $n!$ to the tree factorial $t^!$. Various identities on tree-factorials are derived which clarify the relation between Connes-Moscovici weights and Quantum Field Theory.35p, LaTeX, using epsf for four figures. References updated and typos correctedHigh Energy Physics - TheoryMathematical PhysicsQuantum Algebratext