BRS Cohomology of the Supertranslations in D=4

Abstract

Supersymmetry transformations are a kind of square root of spacetime translations. The corresponding Lie superalgebra always contains the supertranslation operator $ δ= c^α σ^μ_{α\dot β} {\overline c}^{\dot β} (ε^μ)^† $. 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.