On the Hopf algebra structure of perturbative quantum field theories

TL;DR

This paper reveals that renormalization in quantum field theories naturally forms a Hopf algebra structure, providing new insights into the connection between knot theory and renormalization.

Contribution

It demonstrates the intrinsic Hopf algebra structure of renormalization, linking quantum field theory and knot theory in a novel way.

Findings

Renormalization process encodes a Hopf algebra structure.

Establishes a connection between knot theory and renormalization.

Provides a mathematical framework for understanding renormalization.

Abstract

We show that the process of renormalization encapsules a Hopf algebra structure in a natural manner. This sheds light on the recently proposed connection between knots and renormalization theory.