Clifford Algebras and Spinor Operators

Abstract

This paper begins with a historical survey on Clifford algebras and a model on how to start an undergraduate course on Clifford algebras. The Dirac equation and the bilinear covariants are discussed. The Fierz identities are sufficient to reconstruct a Dirac spinor from its bilinear covariants, up to a phase. However, the Weyl and Majorana spinors cannot be reconstructed using the Fierz identities alone. This paper introduces a new concept, the boomerang, for the reconstruction of the Weyl and Majorana spinors. This method reveals a new class of spinors residing in between the Weyl, Majorana and Dirac spinors, namely the flag-dipole spinors.