The Hopf algebra of Feynman diagrams, analyzed by A. Connes and D. Kreimer,
is considered from the perspective of the theory of effective actions and
generalized tau -functions, which describes the action of diffeomorphism an
d shift groups in the moduli space of coupling constants. These considerati
ons provide additional evidence of the hidden group (integrable) structure
behind the standard formalism of quantum field theory.