Yang–Mills functional

Summary

The Yang–Mills functional assigns to a connection on a principal bundle over a compact Riemannian manifold the integral of the squared norm of its curvature. It does not change under gauge transformations. Its critical points are the solutions of the Yang–Mills equations, and its absolute minima include the flat connections. In dimension four its minima in a given bundle are often the instantons, which led to deep results on four-manifolds.