Constraints on mapping the Lounesto’s classes

Abstract

AbstractThe so-called Lounesto’s classification engenders six distinct classes of spinors, divided into two sectors: one composed by regular spinors (single-helicity spinors) and the other composed by singular spinors (comprising dual-helicity spinors). In the present essay we develop a mechanism to fully define the right class within the Lounesto’s classification a spinor belongs to, without necessity to evaluate the 16 bilinear forms. The analysis lies in the following criteria: a judicious inspection of the phases factor present in both spinor’s components. Thus, the machinery developed here works for both regular and singular spinors. Taking advantage of the present algorithm, we analyse, under certain conditions, the possibility to transmute between the six classes.