= Two-component superspace contraction signs
{title2=$\theta\theta,\bar\theta\bar\theta$}
For <left Grassmann derivatives>, $\epsilon^{12}=-\epsilon_{12}=1$, $\theta\theta=\theta^\alpha\theta_\alpha$ and $\bar\theta\bar\theta=\bar\theta_{\dot\alpha}\bar\theta^{\dot\alpha}$, the antisymmetric products are $\theta^\alpha\theta^\beta=-\epsilon^{\alpha\beta}\theta\theta/2$ and $\bar\theta^{\dot\alpha}\bar\theta^{\dot\beta}=\epsilon^{\dot\alpha\dot\beta}\bar\theta\bar\theta/2$. With contractions $\partial^2=\partial^\alpha\partial_\alpha$ and $\bar\partial^2=\bar\partial_{\dot\alpha}\bar\partial^{\dot\alpha}$, both squared derivatives give $-4$ on the matching quadratic monomial. If $\operatorname{Tr}(\sigma^\mu\bar\sigma^\nu)=2\eta^{\mu\nu}$, the mixed bilinear product is $+(\theta\theta)(\bar\theta\bar\theta)\eta^{\mu\nu}/2$. Reversing the metric-relative trace convention reverses this last sign.
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