Let the spin and the charges unify

Abstract

In space of d ordinary and d Grassmann coordinates, with d \ge 15, the charges unify with the spin: the Lorentz group SO(1, d-1) in Grassmann space manifests under certain conditions as SO(1,3) (in d=4 subspace) times SO(10) \supset SU(3) \times SU(2) \times U(1) (in the rest of the space), accordingly the symmetry group of the S- matrix, which is approximatelly unitary in d=4 ordinary subspace, manifests as the direct product of the Poincaré group in d=4 subspace and the group describing charges. (Talk presented at XIX Triangular Meeting on Recent Development in Quantum Theories, Rome, March 1996 and at IWCQIS 96, Dubna, July 1996.)