On “Conformal spinor geometry”: An attempt to “Understand” internal symmetry

Abstract

The natural homomorphism of pure spinors corresponding to a given Clifford algebraC2n to polarized isotropicn-planes of complex Euclidean spaceE2nc is taken as a starting point for the construction of a geometry called spinor geometry where pure spinors are the only elements out of which all tensors have to be constructed (analytically as bilinear polynomials of the components of a pure spinor).C4 andC6 spinor geometry are analyzed, but it seems that C8 spinor geometry is necessary to construct Minkowski spaceM3,1.C6 spinor field equations give rise in Minkowski space to a pair of Dirac equations (for conformal semispinors) presenting ansu(2) internal symmetry algebra. Mass is generated by breaking spontaneously the originalO(4,2) symmetry of the spinor equation.