Self-dual Yang-Mills equations in temporal gauge
= Self-dual Yang-Mills equations in temporal gauge
{title2=$\partial_tA_i=-\frac12\epsilon_{ijk}F_{jk}$}
With orientation $dx^1\wedge dx^2\wedge dx^3\wedge dt$, $\epsilon_{123}=1$, and <temporal gauge> $A_t=0$, the mixed <gauge curvature> is $F_{ti}=\partial_tA_i$. The <self-dual Yang-Mills equations> then have the displayed form. Placing $dt$ first in the orientation reverses the sign, so the metric alone does not specify it.