= Superspace differential realization of N=1 supercharges
{title2=$\{\mathcal Q_\alpha,\bar{\mathcal Q}_{\dot\beta}\}=2\sigma^\mu_{\alpha\dot\beta}\mathcal P_\mu$}
With left <Grassmann derivatives>, define $\mathcal P_\mu=-i\partial_\mu$, $\mathcal Q_\alpha=-i\partial_{\theta^\alpha}-\sigma^\mu_{\alpha\dot\gamma}\bar\theta^{\dot\gamma}\partial_\mu$ and $\bar{\mathcal Q}_{\dot\beta}=i\partial_{\bar\theta^{\dot\beta}}+\theta^\gamma\sigma^\mu_{\gamma\dot\beta}\partial_\mu$. The anticommutators of the derivative parts and of the coordinate parts vanish. Each mixed derivative/coordinate pair contributes $-i\sigma^\mu\partial_\mu$ by the graded product rule, giving the displayed mixed <anticommutator>. Equal-chirality anticommutators vanish, and all these operators commute with translations. Under <Lorentz transformations> their spinor indices transform in conjugate <Weyl spinor> representations, completing the minimal <Super-Poincaré algebra>. A convention for left derivatives is essential to the signs.
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