Hopf algebras and the combinatorics of connected graphs in quantum field theory

TL;DR

This paper explores the use of Hopf algebras to efficiently generate and evaluate connected graphs in quantum field theory, enhancing the combinatorial understanding of n-point functions.

Contribution

It introduces a recursive algorithm for generating connected graphs within the Hopf algebra framework, improving computational methods in quantum field theory.

Findings

Developed a recursive algorithm for connected graph generation

Enhanced the evaluation of Feynman graphs in quantum field theory

Provided a combinatorial and algebraic approach to n-point functions

Abstract

In this talk, we are concerned with the formulation and understanding of the combinatorics of time-ordered n-point functions in terms of the Hopf algebra of field operators. Mathematically, this problem can be formulated as one in combinatorics or graph theory. It consists in finding a recursive algorithm that generates all connected graphs in their Hopf algebraic representation. This representation can be used directly and efficiently in evaluating Feynman graphs as contributions to the n-point functions.