Self-duality implies Yang-Mills equations
= Self-duality implies Yang-Mills equations
{title2=$D_AF=0,\quad *F=\pm F\ \Longrightarrow\ D_A*F=0$}
Both the <self-dual Yang-Mills equations> and the <Anti-self-dual Yang-Mills equations> imply the second-order <Yang-Mills equations> because the <Bianchi identity> holds for every <principal connection>. Finite action is additionally required to call the solution a <Yang-Mills instanton>; the implication itself is a local differential identity.