Self-duality of gauge curvature
= Self-duality of gauge curvature
{title2=$F=*F$}
In oriented Euclidean four-space, gauge curvature is self-dual when $F=*F$. The Hodge star squares to one on two-forms, so this picks its positive eigenspace; the negative eigenspace is <anti-self-duality of gauge curvature>. The <Bianchi identity> then implies the <Yang-Mills equations>, and the action saturates the positive-charge <Yang-Mills instanton Bogomolny bound>.