= Two-dimensional N=(1,1) superspace
{title2=$\mathbb R^{1,1|2}$}
In <light-cone coordinates> $x^\pm$ on two-dimensional <Minkowski spacetime>, add two real odd <Grassmann variables> $\theta^\pm$. With <left Grassmann derivatives>, the <supercharges> and <supersymmetric covariant derivatives> can be represented as
$$
Q_\pm=\partial_{\theta^\pm}+i\theta^\pm\partial_\pm,\qquad D_\pm=\partial_{\theta^\pm}-i\theta^\pm\partial_\pm.
$$
The identity $\{\partial_\theta,\theta\}=1$ gives $Q_\pm^2=i\partial_\pm$, $D_\pm^2=-i\partial_\pm$, $\{Q_+,Q_-\}=\{D_+,D_-\}=0$, and $\{Q_s,D_t\}=0$ for every $s,t$. A <Lorentz boost> acts as $x^\pm\mapsto e^{\pm\omega}x^\pm$, $\theta^\pm\mapsto e^{\pm\omega/2}\theta^\pm$. Thus $D_\pm$ have boost weights $\mp1/2$, and $D_-D_+$ is a <Lorentz scalar>. Since it commutes with both <supercharges>, an equation $iD_-D_+\Phi=W(\Phi)$ for an even scalar <superfield> is <Lorentz invariant> and <supersymmetry> covariant.
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