't Hooft-Polyakov monopole of higher generalized angular momenta

TL;DR

This paper uses quaternionic formulation to analyze the spectral properties of 't Hooft-Polyakov monopoles with higher angular momenta, revealing eigenvalue behaviors, bound states, and Feshbach resonances.

Contribution

It introduces a quaternionic approach to study monopole solutions for various angular momenta and investigates their spectral and resonance properties.

Findings

Eigenvalues tend to 1 as generalized momentum increases

Existence of Feshbach resonance for ω < 1

Calculated partial cross section for ω > 1

Abstract

We recall the quaternionic fomulation, which can simplify the computation of the linearized Yang-Mills-Higgs equation in the background of a 't Hooft-Polyakov monopole. We then study the solutions in the cases $j=0$, $j=1$ and $j\geq 2$ separately. In particular, we investigate the spectral properties of the monopoles. We focus on some of the bound states and show that as the generalized momentum increases, the $k-$th eigenvalue tends to 1. We show the existence of Feshbach resonance for $\om <1$ in the coupled system and calculated the partial cross section when $\om >1$.