Factorization method and the supersymmetric monopole harmonics

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.