Supersymmetry and the rotation group

Abstract

A model invariant under a supersymmetric extension of the rotation group 0(3) is mapped, using a stereographic projection, from the spherical surface S 2 to two dimensional Euclidean space. The resulting model is not translation invariant. This has the consequence that fields that are supersymmetric partners no longer have a degenerate mass. This degeneracy is restored once the radius of S 2 goes to infinity, and the resulting supersymmetry transformation for the fields is now mass dependent. An analogous model on the surface S 4 is introduced, and its projection onto four dimensional Euclidean space is examined. This model in turn suggests a supersymmetric model on (3 + 1) dimensional Minkowski space.