= Supercovariant derivative algebra with left derivatives
{title2=$\{D_\alpha,\bar D_{\dot\beta}\}=2i\sigma^\mu_{\alpha\dot\beta}\partial_\mu$}
For <left Grassmann derivatives>, choose $D_\alpha=\partial_\alpha+i\sigma^\mu_{\alpha\dot\beta}\bar\theta^{\dot\beta}\partial_\mu$ and $\bar D_{\dot\alpha}=\bar\partial_{\dot\alpha}+i\theta^\beta\sigma^\mu_{\beta\dot\alpha}\partial_\mu$. Differentiating the other operator's odd coefficient gives two equal contributions to the mixed <anticommutator>; coefficient-coefficient terms cancel by the <Grassmann algebra>. Thus the mixed <anticommutator> is $2i\sigma^\mu\partial_\mu$, while equal-chirality ones vanish. Also $\bar D(x+i\theta\sigma\bar\theta)=0$, giving the coordinates used in the <chiral-superfield component expansion>. Negating the barred derivative negates the mixed algebra.
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