NDLI: ELKO, Flagpole and Flag-Dipole Spinor Fields, and the Instanton Hopf Fibration

Content Provider	Springer Nature Link
Author	Rocha, R. Silva, J. M. Hoff
Copyright Year	2010
Abstract	In a previous paper we explicitly constructed a mapping that leads Dirac spinor fields to the dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields). ELKO spinor fields are prime candidates for describing dark matter, and belong 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. Such a mapping between Dirac and ELKO spinor fields was obtained in an attempt to extend the Standard Model in order to encompass dark matter. Now we prove that such a mapping, analogous to the instanton Hopf fibration map S3...S7 → S4, indicates that ELKO is not suitable to describe the instanton. We review ELKO spinor fields as type-(5) spinor fields under the Lounesto spinor field classification, explicitly computing the associated bilinear covariants. This paper is also devoted to investigate some formal aspects of the flag-dipole spinor fields, which correspond to the class-(4) under the Lounesto spinor field classification and, in addition, we prove that type-(4) spinor fields — corresponding to flag-dipoles — and ELKO spinor fields — corresponding to flagpoles — can also be entirely described in terms of the Majorana and Weyl spinor fields. After all, by choosing a projection endomorphism of the spacetime algebra $${\mathcal C}\ell_{1,3}$$ it is shown how to obtain ELKO, flagpole, Majorana and Weyl spinor fields, respectively corresponding to type-(5) and -(6) spinor fields, uniquely from limiting cases of a type-(4) — flag-dipole — spinor field, in a similar result obtained by Lounesto.
Ending Page	870
Page Count	24
Starting Page	847
File Format	PDF
ISSN	01887009
e-ISSN	16614909
Journal	Advances in Applied Clifford Algebras
Issue Number	3
Volume Number	20
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2010-05-11
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical Methods in Physics ELKO spinor fields flagdipoles Clifford algebras, spinors Theoretical, Mathematical and Computational Physics instantons Clifford algebras bilinear covariants Applications of Mathematics Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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