Geometry of spinors: doubly-chiral plane-wave expansion

We employ the polar re-formulation of spinor fields to see in a new light their classification into regular and singular spinors, these last also called flag-dipoles, further splitting into the sub-classes of dipoles and flagpoles: in particular, we will study the conditions under which flagpoles may be solutions of the Dirac field equations. We argue for an enlargement of the plane-wave expansion.