The Extended Fock Basis of Clifford Algebra

TL;DR

This paper explores the Extended Fock Basis of Clifford algebras, revealing their structure as a sum of spinor subspaces and analyzing the properties of simple spinors in relation to null planes.

Contribution

It demonstrates that Clifford algebras can be decomposed into spinor subspaces characterized by eigenvectors of , and examines the maximum non-zero coordinates of simple spinors.

Findings

Clifford algebra decomposes into multiple spinor subspaces.

Simple spinors can have up to the size of the maximal totally null plane non-zero coordinates.

Exceptional case for vector spaces with 6 dimensions.

Abstract

We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras introduced in [1]. We show that a Clifford algebra can be seen as a direct sum of multiple spinor subspaces that are characterized as being left eigenvectors of \Gamma. We also show that a simple spinor, expressed in Fock basis, can have a maximum number of non zero coordinates that equals the size of the maximal totally null plane (with the notable exception of vectorial spaces with 6 dimensions).