Cauchy matrix approach to the SU(2) self-dual Yang--Mills equation

TL;DR

This paper develops a Cauchy matrix method to construct explicit solutions for the SU(2) self-dual Yang--Mills equation, advancing analytical techniques in gauge theory.

Contribution

It introduces a novel Cauchy matrix approach combined with Sylvester equations to generate explicit solutions for the self-dual Yang--Mills equation.

Findings

Explicit solutions derived under complex variable constraints

Method bridges Sylvester equations with gauge theory solutions

Broad class of solutions constructed for SU(2) equations

Abstract

The Cauchy matrix approach is developed to solve the SU(2) self-dual Yang--Mills equation. Starting from a Sylvester matrix equation coupled with certain dispersion relation for infinite coordinates, the self-dual Yang--Mills equation under Yang's formulation is constructed. By imposing further constraints on complex independent variables, a broad class of explicit solutions are obtained.