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arXiv · 0903.2815

From Dirac Action to ELKO Action

J. M. Hoff da Silva·Roldao da Rocha
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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.

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J. M. Hoff da Silva, Roldao da Rocha. 2009-03-16. From Dirac Action to ELKO Action. https://doi.org/10.1142/s0217751x09044218

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