We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras introduced in [1] that allows to replace the traditional multivector expansion of C ℓ(g) with an expansion in terms of simple spinors. We show that a Clifford algebra with 2m generators is the direct sum of 2m spinor subspaces S partially characterized as being left eigenvectors of Γ; furthermore the traditional isomorphism between simple spinors and totally null planes holds only within one of this subspaces. We also show that simple spinors can form spinor subspaces of dimension equal to that of the maximal totally null plane of the corresponding vector space (with the notable exception of vectorial spaces with 6 dimensions).
The extended Fock basis of Clifford algebra
BUDINICH, MARCO
2011-01-01
Abstract
We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras introduced in [1] that allows to replace the traditional multivector expansion of C ℓ(g) with an expansion in terms of simple spinors. We show that a Clifford algebra with 2m generators is the direct sum of 2m spinor subspaces S partially characterized as being left eigenvectors of Γ; furthermore the traditional isomorphism between simple spinors and totally null planes holds only within one of this subspaces. We also show that simple spinors can form spinor subspaces of dimension equal to that of the maximal totally null plane of the corresponding vector space (with the notable exception of vectorial spaces with 6 dimensions).Pubblicazioni consigliate
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