On the equivalence of the Lagrangians of massless dirac and supersymmetrical particles

The classical equivalence between the Lagrangians of massless spinning and supersymmetrical particles presented in terms of u _A and Grassmannian _A Weyl spinor variables is established. It is shown that the condition of the inverse Higgs effect for a spinor invariant superform leads to the extension of the Penrose representation and the realization of fermionic string variables in terms of superstring variables. New superfield formulations of the actions for particles and strings invariant under local (world-sheet) and global (spacetime) supersymmetrics are suggested.