On Explicit Point Multi-Monopoles in SU(2) Gauge Theory

TL;DR

This paper constructs explicit multi-monopole solutions in SU(2) gauge theory, generalizing the Wu-Yang monopole to configurations with multiple monopoles and anti-monopoles at arbitrary positions.

Contribution

It provides a geometric method to explicitly embed multi-center Dirac monopole configurations into SU(2) gauge theory, extending known solutions.

Findings

Explicit multi-monopole solutions in SU(2) gauge theory.

Generalization of Wu-Yang monopole to multiple centers.

Solutions applicable to arbitrary monopole and anti-monopole arrangements.

Abstract

It is well known that the Dirac monopole solution with the U(1) gauge group embedded into the group SU(2) is equivalent to the SU(2) Wu-Yang point monopole solution having no Dirac string singularity. We consider a multi-center configuration of m Dirac monopoles and n anti-monopoles and its embedding into SU(2) gauge theory. Using geometric methods, we construct an explicit solution of the SU(2) Yang-Mills equations which generalizes the Wu-Yang solution to the case of m monopoles and n anti-monopoles located at arbitrary points in R^3.