Shuffling quantum field theory

TL;DR

This paper explores shuffle identities in Feynman graphs within quantum field theory using Hopf algebra structures, focusing on the vertex function in massless Yukawa theory.

Contribution

It introduces a novel approach to understanding Feynman graph identities through Hopf algebra, specifically applied to massless Yukawa theory.

Findings

Established shuffle identities for Feynman graphs

Applied Hopf algebra framework to quantum field theory

Provided insights into vertex functions in Yukawa theory

Abstract

We discuss shuffle identities between Feynman graphs using the Hopf algebra structure of perturbative quantum field theory. For concrete exposition, we discuss vertex function in massless Yukawa theory.