A hint towards mass dimension one Flag-dipole spinors

R J Bueno Rogerio,C H Coronado Villalobos,A R Aguirre

doi:10.1140/epjc/s10052-019-7518-5

Abstract

In this report we advance in exploring further details concerning the formal aspects of the construction of a Flag-dipole spinor. We report a (re-)definition of the dual structure which provide a Lorentz invariant and non-null norm, ensuring a local theory. With the new dual structure at hands, we look towards define relevant physical amounts, e.g., spin sums and quantum field operator. As we will see, the Flag-dipole and the Elko’s theory are quite familiar. In this vein, it is possible, via a matrix transformation, to write Flag-dipole spinors in terms of Elko spinor, evincing that both spinors are physically related and some physical amounts may be stated as equivalent.

Highlights

Spinors constitute a comprehensive mathematical object of study, with several applications in physics
In this communication we have developed a deeper analysis of the recently proposed Flag-dipole spinors in Ref. [9], by providing new features, as the definition of a dual structure, which leads to a Lorentz invariant and non-null norm
We have faced a difficulty in fixing the phase parameters due to the fact that Flag-dipole spinors do not compose a complete set of eigenspinors of discrete symmetries

Summary

Introduction

Spinors constitute a comprehensive mathematical object of study, with several applications in physics. Such mathematical objects are the rudimentary ingredient to describe fermionic particles. We introduce new features concerning the Flag-dipole spinors recently proposed in [9]. There is a strong connection between the Flag-dipole spinors and the Elko spinors, by defining some mathematical conditions it is possible to transmute among type-4 and Elko spinors, we emphasize that the last above mentioned spinors are shown to be slightly related to Elko just by a matrix transformation. We highlight that the seminal attempt to establish a connection among flag-dipole spinors and Elko, pointing out some algebraic and geometric considerations, was developed in [11]. We develop allusive comments showing the connection among Elko and Flag-dipole spinors.

Setting up the notation

A brief overview on Flag-dipole spinors

On the set-up of the adjoint structure

A guide for a new adjoint

An attempt to define the Flag-dipole quantum field

Concluding remarks