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Standard-model symmetry in complexified spacetime algebra

Jose B. Almeida
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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.

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Jose B. Almeida. 2003-08-02. Standard-model symmetry in complexified spacetime algebra. https://arxiv.org/abs/math/0307165

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