  In recent years a Hopf algebraic structure underlying the process of
renormalization in quantum field theory was found. It led to a Birkhoff
factorization for (regularized) Hopf algebra characters, i.e. for Feynman
rules. In this work we would like to show that this Birkhoff factorization
finds its natural formulation in terms of a classical r-matrix, coming from a
Rota-Baxter structure underlying the target space of the regularized Hopf
algebra characters. Working in the rooted tree Hopf algebra, the simple case of
the Hopf subalgebra of ladder trees is treated in detail. The extension to the
general case, i.e. the full Hopf algebra of rooted trees or Feynman graphs is
briefly outlined.
