Questing for Algebraic Mass Dimension One Spinor Fields

TL;DR

This paper explores new classes of spinor fields with mass dimension one in Minkowski spacetime, extending the algebraic classification using Lounesto's scheme and the Fierz aggregate to identify novel spinor solutions.

Contribution

It generalizes the spinor classification scheme to include new mass dimension one spinors, emphasizing the role of the spinor operator in their construction.

Findings

New classes of mass dimension one spinors identified

Generalized classification scheme developed

Role of spinor operator clarified

Abstract

This work deals with new classes of spinors of mass dimension one in Minkowski spacetime. In order to accomplish it, the Lounesto classification scheme and the inversion theorem are going to be used. The algebraic framework shall be revisited by explicating the central point performed by the Fierz aggregate. Then the spinor classification is generalized in order to encompass the new mass dimension one spinors. The spinor operator is shown to play a prominent role to engender the new mass dimension one spinors, accordingly.