Bogolubov's Recursion and Integrability of Effective Actions

TL;DR

This paper explores the hidden integrable group structure in quantum field theory through the Hopf algebra of Feynman diagrams, effective actions, and generalized tau-functions, revealing deeper mathematical symmetries.

Contribution

It introduces a novel perspective connecting Hopf algebra structures with integrability and effective actions in quantum field theory.

Findings

Evidence of hidden integrable group structures in quantum field theory

Connection between Hopf algebra of Feynman diagrams and generalized tau-functions

Insights into the symmetry properties 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.