Combinatorics of n-point functions via Hopf algebra in quantum field theory

TL;DR

This paper introduces a Hopf algebra-based coproduct approach to derive relations between different n-point functions in quantum field theory, offering a more intrinsic and computationally efficient alternative to traditional methods.

Contribution

It presents a novel coproduct method within Hopf algebra to simplify and accelerate calculations of n-point functions in quantum field theory.

Findings

Derives simple relations between n-point functions using Hopf algebra

Provides algorithms that are more efficient than traditional functional methods

Enables efficient tree level computations in quantum field theory

Abstract

We use a coproduct on the time-ordered algebra of field operators to derive simple relations between complete, connected and 1-particle irreducible n-point functions. Compared to traditional functional methods our approach is much more intrinsic and leads to efficient algorithms suitable for concrete computations. It may also be used to efficiently perform tree level computations.