What does a magnetic monopole field "look like"?

If magnetic monopoles exist, they are predicted to have large charges--or equivalently, a large coupling constant, which means that perturbative models don't converge.

While I get that that makes it very difficult to calculate things like the binding energy of monopolium, is it at least possible to make qualitative statements about what magnetostatics, the strongly-coupled analog of electrostatics, looks like? E.g., can you still reasonably approximate the strength of a monopole field as $$\frac{1}{r^2}$$ down to arbitrarily small lengths?

• Yes; what of it? Sep 18, 2021 at 19:55

($$\mu_0=1$$):
$$\nabla \cdot \vec{B} = \rho$$
where $$\rho$$ is the magnetic charge density, has a solution:
$$\vec{B} = \frac{1}{4\pi}\frac{q}{r^2}$$
for point particles, i.e: $$\rho = \delta(r)$$, and $$q$$ is the magnetic charge. In fact, this is exactly what we want. We designed the magnetic monopole to act like a electric monopole because we saw it would be nice to have symmetry between them.