2007/11/07 by Roldão da Rocha, Roldao da Rocha, J. M. Hoff da Silva +1 · 7 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Dark Matter and Cosmic Phenomena #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.MP #msc:15A66 #msc:81Q05
paper · pdf · doi:10.1063/1.2825840
published as J.Math.Phys.48:123517,2007 · 10 pages
arxiv created 2007/11/07 · openalex publication_date 2007/12/01 · arxiv updated 2009/12/01 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/02
Dual-helicity eigenspinors of the charge conjugation operator [eigenspinoren des ladungskonjugationsoperators (ELKO) spinor fields] belong—together with Majorana spinor fields—to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class (5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three, respectively, corresponding to flagpole, flag-dipole, and Weyl spinor fields. This paper is devoted to investigate and provide the necessary and sufficient conditions to map Dirac spinor fields to ELKO, in order to naturally extend the standard model to spinor fields possessing mass dimension 1. As ELKO is a prime candidate to describe dark matter, an adequate and necessary formalism is introduced and developed here, to better understand the algebraic, geometric, and physical properties of ELKO spinor fields, and their underlying relationship to Dirac spinor fields.