Factorization method and the supersymmetric monopole harmonics

TL;DR

This paper develops a supersymmetric framework for analyzing a charged particle on a sphere with a monopole, using factorization methods to solve the system both classically and quantum mechanically.

Contribution

It introduces a novel application of the factorization method within supersymmetric sigma models to solve monopole dynamics on curved manifolds.

Findings

Successfully formulated classical and quantum dynamics of the system

Applied factorization method to integrate the equations of motion

Extended supersymmetric techniques to monopole field configurations

Abstract

We use the general $N = 1$ supersymmetric formulation of one dimensional sigma models on non trivial manifolds and its subsequent quantization to formulate the classical and quantum dynamics of the $ N= 2 $ supersymmetric charged particle moving on a sphere in the field of a monopole. The factorization method accommodated with the general covariance and it is used to integrate the corresponding system.