Bogomolny equations

In mathematics, the Bogomolny equations for magnetic monopoles are the equations F_A = *D_Aφ, where F_A is the curvature of a connection A on a G-bundle over a 3-manifold M, φ is a section of the corresponding adjoint bundle and * is the Hodge star operator on M. These equations are named after E. B. Bogomolny.

The equations are a dimensional reduction of the self-dual Yang–Mills equations in four dimensions and correspond to global minima of the appropriate action. If M is closed there are only trivial (i.e., flat) solutions.