Leading log expansion of combinatorial Dyson Schwinger equations

TL;DR

This paper explores the leading log expansion of combinatorial Dyson Schwinger equations within a Hopf algebra framework, revealing that such expansions simplify to power-law expressions when mapped to a polynomial algebra.

Contribution

It introduces a novel mapping of Dyson Schwinger equations into a polynomial algebra that simplifies the leading log expansion to power-law forms.

Findings

Leading log expansions become simple power-law expressions

Mapping to polynomial algebra simplifies complex combinatorial equations

Provides a new algebraic approach to Dyson Schwinger equations

Abstract

We study combinatorial Dyson Schwinger equations, expressed in the Hopf algebra of words with a quasi shuffle product. We map them into an algebra of polynomials in one indeterminate L and show that the leading log expansion one obtains with such a mapping are simple power law like expression