= Nahm equations
{c}
{title2=$\dot A_a=\tfrac12\epsilon_{abc}[A_b,A_c]$}
For three Lie-algebra-valued functions of one variable, the <Nahm equations> are
$$
\dot A_a=\frac12\epsilon_{abc}[A_b,A_c].
$$
They arise by taking a solution of the <ASDYM equations> with orientation $dx^1\wedge dx^2\wedge dx^3\wedge dt$, imposing independence of $x^1,x^2,x^3$, and setting $A_t=0$ by a local <Yang-Mills gauge transformation>. Then $F_{ab}=[A_a,A_b]$, $F_{a t}=-\dot A_a$, and <anti-self-duality of gauge curvature> gives the displayed equations. The opposite orientation reverses their sign.
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