However, the vector potential cannot be defined globally precisely because the divergence of the magnetic field is proportional to the Dirac delta function at the origin. We must define one set of functions for the vector potential on the "northern hemisphere" (the half-space z > 0 above the particle), and another set of functions for the "southern hemisphere". These two vector potentials are matched at the "equator" (the plane z = 0 through the particle), and they differ by a gauge transformation. The wave function of an electrically charged particle (a "probe charge") that orbits the "equator" generally changes by a phase, much like in the Aharonov–Bohm effect. This phase is proportional to the electric charge q e of the probe, as well as to the magnetic charge q m of the source. Dirac was originally considering an electron whose wave function is described by the Dirac equation.