Magnetic Monopoles in (Noncommutative) Quantum Mechanics

We utilize the close relation between the complex space ${\mathbf{\text{C}}}^2$ and the real space ${\mathbf{\text{R}}}^3$ to reformulate quantum mechanics in a manner which allows to, either or both, describe magnetic monopoles and quantize the underlying space, obtaining (noncommutative) quantum mechanics (with magnetic monopoles).