Perturbation theory for nonlinear equations

TL;DR

This paper develops a perturbative approach for solving nonlinear equations, including those in field theories, using diagrammatic representations, and demonstrates the method with Yang-Mills equations.

Contribution

It introduces a new perturbative formalism with graphical diagram representation applicable to a broad class of nonlinear equations including field theory equations.

Findings

Perturbative solutions can be systematically constructed for nonlinear equations.

Diagrammatic representation simplifies understanding of solution structure.

Application to Yang-Mills equations illustrates the formalism's effectiveness.

Abstract

For a wide class of nonlinear equations a perturbative solution is constructed. This class includes equations of motion of field theories. The solution possesses a graphical representation in terms of diagrams. To illustrate the formalism we consider the Yang-Mills field equations.