AN ANALYSIS OF FIERZ IDENTITIES, FACTORIZATION AND INVERSION THEOREMS

We show that the full set of Fierz identities which are used to comput e electro-weak interactions reported hy Y. Takahashi can he considered as particular cases of the Clifford product between multivector Carta n maps. Moreover, we think that our approach can be generalized to hig her-dimensional models. We discuss the factorization and inversion the orems for the recovery of the spinor from its multivectorial Cartan ma p. A new classification given by P. Lounesto is applied to the recover ed spinors for Cl1,3 space-time symmetry and SU(2) x U(1) isotopic gro up.