A hint towards mass dimension one Flag-dipole spinors

TL;DR

This paper explores the formal structure of Flag-dipole spinors, proposing a new dual definition that ensures Lorentz invariance and relates these spinors to Elko spinors, with implications for quantum field theory.

Contribution

It introduces a new dual structure for Flag-dipole spinors that guarantees Lorentz invariance and establishes a physical relation to Elko spinors through matrix transformations.

Findings

New dual structure for Flag-dipole spinors ensuring Lorentz invariance

Flag-dipole and Elko spinors are related via matrix transformation

Physical quantities can be equivalently expressed for both spinor types

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 familar. 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.