Geometry of the magnetic monopole

It is shown that the vector potential of a magnetic monopole can be obtained from consideration of the Berry phase in a new perspective. The two-component complex wavefunction can be characterized by a single CP1 projective coordinate w on the projected compactified complex plane. So the vector potential on the sphere is expressed solely in terms of w. The projective structure is more evident in this consideration. We also attempt to demonstrate that the wavefunctions can be coupled to yield a monopole with a doubling of the magnetic charge in a simple case. Generalization from a complex phase to a quaternionic phase is discussed.