''Conformal Spinor Geometry'': An Attempt to ''Understand'' Internal Symmetry

摘要

The natural homomorphism of pure spinors corresponding to a given Clifford algebra Csub(2n) to polarized isotropic n-planes of complex Euclidean space Esub(2n)sup(c) 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 polynomia of the components of a pure spinor). C sub 4 and C sub 6 spinor geometry are analyzed but it seems that C sub 8 spinor geometry is necessary to construct Minkowski space Msup(3,1). C sub 6 spinor field equations give rise in Minkowski space to a pair of Dirac equations (for conformal semispinors) presenting an SU(2) internal symmetry algebra. Mass is generated by spontaneously breaking the original O(4,2) symmetry of the spinor equation. (Atomindex citation 14:743551)