# Mathematical renormalization in quantum electrodynamics via noncommutative generating series

## TL;DR

This paper explores a noncommutative formal power series approach to understand the combinatorial structure of renormalization in quantum electrodynamics, especially at singularities of related differential equations.

## Contribution

It introduces a novel application of noncommutative generating series to analyze the combinatorial aspects of QED renormalization at singular points.

## Key findings

- Provides a new mathematical framework for renormalization analysis.
- Identifies combinatorial structures underlying QED singularities.
- Enhances understanding of differential equations in quantum field theory.

## Abstract

In this work, we focus on on the approach by noncommutative formal power series to study the combinatorial aspects of the renormalization at the singularities in $\{0,1,+\infty\}$ of the solutions of nonlinear differential equations involved in quantum electrodynamics.