From Dirac Action to ELKO Action

Details From Dirac Action to ELKO Action From Dirac Action to ELKO Action

2009-03-16

arxiv.org/abs/0903.2815v1

Int.J.Mod.Phys.A24:3227-3242,2009

Physics

Mathematical Physics

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

Scientific paper

10.1142/S0217751X09044218

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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