FROM PURE SPINORS TO FERMION'S - PHYSICS

The questions defining pure spinors are interpreted as questions of motion of fermion multiplets in momentum spaces which, in a constructive approach based on pure spinors, naturally result lorentzian and ending up at P = R^1,9. The equations found are most of those postulated ad hoc in physics for the interpretation of elementary particle phenomology. It is found in this way that several of the observed elementary particle properties derive from the 3 complex division algebras. Precisely complex numbers generate the U(1) at the origin of charged fermions, steadily appearing in changed-neutral pairs (of fermions or of fermion multiplets); quaternions generate internal symmetry SU(2) and SU(2)_L and are at the origin of the 3 families of leptons; octonions generate SU(3) both flavour and color.

The real division algebra (Majorana spinors) might be correlated with the possible origin of black matter.

The resulting momentum spaces result compact isomorphic to invariant mass spheres imbedded in each other and the mass values are naturally increasing with the dimension of the corresponding fermion multiplets.

Further possible role of pure spinors are presented and discussed.