THE SUPERPARTICLE AND THE LORENTZ GROUP

We present a unified group-theoretical framework for superparticle theories. This explains the origin of the "twistor-like" variables that have been used in trading the superparticle'S kappa-symmetry for world-line supersymmetry. We show that these twistor-like variables naturally parametrise the coset space G/H, where G is the Lorentz group SO up (1, d-1) and H is its maximal subgroup, This space is a compact manifold, the sphere S(d-2). Our group-theoretical construction gives the proper covariantisation of a fixed light-cone frame and clarifies the relation between target-space and world-line supersymmetries.