Let the spin and the charges unify

TL;DR

This paper explores how, in a high-dimensional Grassmann space, charges can unify with spin, leading to a symmetry group structure that combines Lorentz and gauge groups, with implications for the S-matrix in quantum theories.

Contribution

It demonstrates that in a 15-dimensional Grassmann space, the Lorentz group can manifest as a product of spacetime and gauge symmetry groups, unifying charges with spin.

Findings

Charges unify with spin in high-dimensional Grassmann space.

The symmetry group of the S-matrix decomposes into spacetime and charge groups.

The Lorentz group manifests as a product of SO(1,3) and SO(10) in specific subspaces.

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 Poincar\'e 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.)