Standard-model symmetry in complexified spacetime algebra

Abstract

Complexified spacetime algebra is defined as the geometric (Clifford) algebra of spacetime with complex coefficients, isomorphic ${\mathcal{G}}_{1,4}$. By resorting to matrix representation by means of Dirac-Pauli gamma matrices, the paper demonstrates isomorphism between subgroups of CSTA and SU(3). It is shown that the symmetry group of those subgroups is indeed $U(1)\otimes SU(2)\otimes SU(3)$ and that there are 4 distinct copies of this group within CSTA.

8 pages, revised and extended compared to V.1