The Possible Role of Pure Spinors in Some Sectors of Particle Physics
  The equations defining pure spinors are interpreted as equations of motion formulated on the lightcone of a ten-dimensional, lorentzian, momentum space. Most of the equations for fermion multiplets, usually adopted by particle physics, are then naturally obtained and their properties like internal symmetries, charges, families appear to be due to the correlation of the associated Clifford algebras, with the 3 complex division algebras: complex numbers at the origin of U(1) and charges; quaternions at the origin of SU(2); families and octonions at the origin of SU(3). Pure spinors instead could be relevant not only because the underlying momentum space results compact, but also because it may throw light on some aspects of particle physics, like: masses, charges, constaint relations, supersymmetry and epistemology. 
Paolo Budinich