Bogolubov's Recursion and Integrability of Effective Actions

Abstract

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 and shift groups in the moduli space of coupling constants. These considerations provide additional evidence of the hidden group (integrable) structure behind the standard formalism of quantum field theory.