  Supersymmetry transformations are a kind of square root of spacetime
translations. The corresponding Lie superalgebra always contains the
supertranslation operator $ \delta = c^{\alpha} \sigma^{\mu}_{\alpha \dot
\beta} {\overline c}^{\dot \beta} (\epsilon^{\mu})^{\dag} $. We find that the
cohomology of this operator depends on a spin-orbit coupling in an SU(2) group
and has a quite complicated structure. This spin-orbit type coupling will turn
out to be basic in the cohomology of supersymmetric field theories in general.
