From Dirac Action to ELKO Action

Abstract

A fundamental action, representing a mass dimension-transmuting operator between Dirac and ELKO spinor fields, is performed on the Dirac Lagrangian, in order to lead it into the ELKO Lagrangian. Such a dynamical transformation can be seen as a natural extension of the Standard Model that incorporates dark matter fields. The action of the mass dimension-transmuting operator on a Dirac spinor field, that defines and introduces such a mapping, is shown to be a composition of the Dirac operator and the non-unitary transformation that maps Dirac spinor fields into ELKO spinor fields, defined in a previous paper. This paper gives allowance for ELKO, as a candidate to describe dark matter, to be incorporated in the Standard Model. It is intended to present for the first time, up to our knowledge, the dynamical character of a mapping between Dirac and ELKO spinor fields, transmuting the mass dimension of spin one-half fermionic fields from 3/2 to 1 and from 1 to 3/2.

17 pages, Int.J.Mod.Phys.A (2009), in press

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• The theory of local mass dimension one fermions of spin one half
• Spinor Dark Energy and Cosmological Coincidence Problem
• Dynamical dispersion relation for ELKO dark spinor fields
• Exotic Dark Spinor Fields
• Exploring Elko typical signature
• A modified theory of gravity with torsion and its applications to cosmology and particle physics
• The most general cosmological dynamics for ELKO Matter Fields
• Conformal Gravity with the most general ELKO Matter
• Localization of 5D Elko Spinors on Minkowski Branes
• Lorentz invariant dark-spinor and inflation
• Zero Energy of Plane-Waves for ELKOs
• Causal propagation for ELKO fields
• Revealing how different spinors can be: the Lounesto spinor classification
• $\Lambda (t)$ cosmology induced by a slowly varying Elko field
• A new approach on the stability analysis in ELKO cosmology
• Constraints on mass dimension one fermionic dark matter from the Yukawa interaction
• ELKO and Dirac Spinors seen from Torsion
• Localization of five-dimensional Elko spinors with non-minimal coupling on thick branes
• Elko and mass dimension one field of spin one half: causality and Fermi statistics
• Dark spinor model with torsion and cosmology
• The most general ELKO Matter in torsional f(R)-theories
• Attractor behaviour in ELKO cosmology
• Causality for ELKOs
• Weyl and Majorana Spinors as Pure Goldstone Bosons
• Constraints on mapping the Lounesto's Classes
• Polar Form of Spinor Fields from Regular to Singular: the Flag-Dipoles
• A hint towards mass dimension one Flag-dipole spinors
• 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
• Spinor Fields, Singular Structures, Charge Conjugation, ELKO and Neutrino Masses
• ELKO in Polar Form
• Symmetries and unitary interactions of mass dimension one fermionic dark matter
• Some Remarks on dual helicity flag-dipole spinors
• The Heisenberg spinor field classification and its interplay with the Lounesto's classification
• Generalized Elko Theory
• An alternative approach concerning Elko spinors and the hidden unitarity
• Type-4 spinors: transmuting from Elko to single-helicity spinors
• The Tensorial Connections
• Localization of five-dimensional Elko Spinors on dS/AdS Thick Branes
• Re-normalizable Chern-Simons Extension of Propagating Torsion Theory
• The Restricted Inomata-McKinley spinor-plane, homotopic deformations and the Lounesto classification
• Geometry of spinors: doubly-chiral plane-wave expansion
• Necessity of Tensorial Connections for Spinorial Systems
• Chern-Simons Extension of ESK Theory