Runge-Kutta methods and renormalization

TL;DR

This paper explores the link between algebraic structures in renormalization theory and Runge-Kutta methods, demonstrating how B-series can be used for renormalization and solving certain nonlinear PDEs.

Contribution

It establishes a novel connection between rooted tree algebra in renormalization and numerical methods, extending B-series applications to PDEs.

Findings

Rooted tree algebra relates to renormalization and Runge-Kutta methods.

B-series framework enables renormalization of a toy quantum field theory model.

B-series can be applied to solve specific nonlinear partial differential equations.

Abstract

A connection between the algebra of rooted trees used in renormalization theory and Runge-Kutta methods is pointed out. Butcher's group and B-series are shown to provide a suitable framework for renormalizing a toy model of field the ory, following Kreimer's approach. Finally B-series are used to solve a class of non-linear partial differential equations.