Geometry of spinors: doubly-chiral plane-wave expansion

TL;DR

This paper explores the geometric classification of spinors using a polar reformulation, examining conditions for flagpole solutions of the Dirac equation and proposing an expanded plane-wave expansion approach.

Contribution

It introduces a new geometric perspective on spinor classification and extends the plane-wave expansion to include flagpole solutions of the Dirac equation.

Findings

Classification of spinors into regular and singular types.

Conditions for flagpole spinors as solutions to Dirac equations.

Proposal of an enlarged plane-wave expansion for spinors.

Abstract

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.