From Dirac spinor fields to ELKO
arXiv:0711.1103 · doi:10.1063/1.2825840
Abstract
Dual-helicity eigenspinors of the charge conjugation operator (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 one. 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.
10 pages
References in corpus (21)
- Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
- Dark matter: A spin one half fermion field with mass dimension one?
- Discovery of a Ringlike Dark Matter Structure in the Core of the Galaxy Cluster Cl 0024+17
- Where are ELKO Spinor Fields in Lounesto Spinor Field Classification?
- The Einstein-Cartan-Elko system
- Theory of Neutral Particles: Mclennan-Case Construct for Neutrino, Its Generalization, and a New Wave Equation
- Algebraic and Dirac-Hestenes Spinors and Spinor Fields
- The quadratic spinor Lagrangian, axial torsion current, and generalizations
- The Bundles of Algebraic and Dirac-Hestenes Spinor Fields
- Hidden Consequence of Active Local Lorentz Invariance
- Supernova 1987A did not test the neutrino mass hierarchy
- A Quadratic Spinor Lagrangian for General Relativity
- The Construction of Spinors in Geometric Algebra
- Dark matter, and its darkness
- Extended set of Majorana spinors, a new dispersion relation, and a preferred frame
- Quantum tomography for Dirac spinors
- From Spinor Geometry to Complex General Relativity
- Majorana Dark Matter
- Twistors, special relativity, conformal symmetry and minimal coupling - a review
- Revisiting Clifford algebras and spinors II: Weyl spinors in Cl(3,0) and Cl(0,3) and the Dirac equation
- A demonstration that the observed neutrinos are not Majorana particles
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- The most general cosmological dynamics for ELKO Matter Fields
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- Constraints on mass dimension one fermionic dark matter from the Yukawa interaction
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- The most general ELKO Matter in torsional f(R)-theories
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- Weyl and Majorana Spinors as Pure Goldstone Bosons
- On a local mass dimension one Fermi field of spin one-half and the theoretical crevice that allows it
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- Spin-half mass dimension one fermions and their higher-spin generalizations
- Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions
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- Mass dimension one fermions and their gravitational interaction
- Weakly-Interacting Massive Particles in Torsionally-Gravitating Dirac Theory
- Non-standard Dirac equations for non-standard spinors
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- Generalized Elko Theory
- An alternative approach concerning Elko spinors and the hidden unitarity
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- Dark matter, Elko fields and Weinberg's quantum field theory formalism
- Essential Fierz identities for a fermionic field
- The Restricted Inomata-McKinley spinor-plane, homotopic deformations and the Lounesto classification
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- Remarks on mass dimension one fermions: The underlying aspects, bilinear forms, Spinor Classification and RIM decomposition