N=4 supersymmetric quantum mechanics with magnetic monopole

We propose an N=4 supersymmetric quantum mechanics of a charged particle on a sphere in the background of Dirac magnetic monopole and study the system in the CP(1) model approach. By using the Dirac quantization method, we explicitly calculate the symmetry algebra taking the operator ordering ambiguity into consideration. We find that it is given by the superalgebra su(1|2)×su(2)rot. We also show that the Hamiltonian can be written in terms of the Casimir invariant of su(2)rot algebra. Using this relation and analyzing the lower bound for angular momentum, we find the energy spectrum. We, then, examine the ground energy sector to find that the N=4 supersymmetry is spontaneously broken to N=2 for certain values of the monopole charge.