Constraints on mapping the Lounesto's Classes

Abstract

The 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.

10 pages, 3 tables, to appear in EPJC

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Cited by in corpus (16)

• Polar Form of Spinor Fields from Regular to Singular: the Flag-Dipoles
• Regular spinors and fermionic fields
• A hint towards mass dimension one Flag-dipole spinors
• Singular spinors and their connection
• Revisiting Takahashi's inversion theorem in discrete symmetry-based dual frameworks
• Hearing the shape of inequivalent spin structures and exotic Dirac operators
• Flag-dipole spinors: On the dual structure derivation and $\mathcal{C}$, $\mathcal{P}$ and $\mathcal{T}$ symmetries
• From Dipole spinors to a new class of mass dimension one fermions
• Propagators Beyond The Standard Model
• Subliminal aspects concerning the Lounesto's classification
• Singular spinors as expansion coefficients of local spin-half fermionic and bosonic fields: On the two-fold Wigner degeneracy
• Exploiting new classes of mass-dimension one fermions
• Spin-half bosonic classification
• Spinorial structures, discrete symmetries and some consequences
• The Most General Propagator in Quantum Field Theory
• Unraveling the Physical Meaning Behind Elko's Dual structure