Construction of the fermionic vacuum and of fermionic operators of creation and annihilation in the theory of algebraic spinors

摘要

We introduced fermionic variables in complex modules over real Cliffordalgebras of even dimension which are analog of the Witt basis. We builtprimitive idempotents which are a set of equivalent Clifford vacuums. It isshown that the modules are decomposed into direct sum of minimal left idealsgenerated by these idempotents and that the fermionic variables can beconsidered as more fundamental mathematical objects than spinors.