The 1/r thing is just emergent from it being a 2d space, since the surface area of a 2d ball goes as 'r', a divergenceless field goes as 1/r (since the flux thr

The 1/r thing is just emergent from it being a 2d space, since the surface area of a 2d ball goes as 'r', a divergenceless field goes as 1/r (since the flux through any contour around the particle ought to be constant). In 3d this would correspond to 1/r^2. The hairy ball theorem is an interesting point. Maybe to equate particles with vortices we have to work in 4d spacetime, since that theorem only applies to even-dimensional spheres?