Yang–Mills equations

Summary

The Yang–Mills equations are the field equations of a gauge theory: they are nonlinear partial differential equations for a connection on a principal bundle. They are the Euler–Lagrange equations of the Yang–Mills functional, the integral of the squared norm of the curvature. For the circle group they reduce to Maxwell's equations in vacuum, and for non-abelian groups they describe the strong and weak forces. In dimension four their self-dual solutions, the instantons, led to deep results on the topology of four-manifolds.