= Self-dual Yang-Mills equations
{title2=$F=*F$}
= SDYM equations
{c}
{synonym}
The self-dual <Yang-Mills equations> require a <gauge curvature> two-form to have positive <Hodge star operator> eigenvalue on an oriented Riemannian four-manifold. By the <Bianchi identity>, they imply the full second-order <Yang-Mills equations>. Smooth finite-action solutions saturate the <Yang-Mills instanton Bogomolny bound>. Reversing orientation exchanges this equation with the <Anti-self-dual Yang-Mills equations>.
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