Abstract
We show that the full set of Fierz identities which are used to compute electro-weak interactions reported by Y. Takahashi can be considered as particular cases of the Clifford product between multivector Cartan maps. Moreover, we think that our approach can be generalized to higher-dimensional models. We discuss the factorization and inversion theorems for the recovery of the spinor from its multivectorial Cartan map. A new classification given by P. Lounesto is applied to the recovered spinors for Cl1,3 space-time symmetry and SU(2)×U(1) isotopic group.
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