A new class of mass dimension one fermions

Abstract

These are notes on the square root of a 4 × 4 identity matrix and associated quantum fields of spin one half. The method is illustrated by constructing a new mass dimension one fermionic field. The presented field is local. The field energy is bounded from below. It is argued that these fermions are a first-principle candidate for dark matter with an unsuppressed quartic self-interaction.

Spinorial discrete symmetries and adjoint structures

“…Such a result is general, encompassing any spinor and proving that the parity operator is is closely connected with class-2 spinors, a specific class responsible for encompass expansion coefficients ensuring locality for the quantum fields. Remarkable examples about what was previously discussed can be found in [3,[22][23][24][25], showing the consistency of the comments around equation (10).…”

“…Such a task is accomplished by invoking duals built upon discrete symmetries and also its combinations. As far we know, the evasion procedure of the dual structure advocated by Lounesto, it is often a valuable and a necessary mathematical mechanism to unveil new and relevant physics associated with spinors, especially regarding the cases in [3,22,23].…”

Regular spinors and fermionic fields

“…[7]. By the same token, recently new fermionic fields, with well behaved quantum counterparts have been found making use of different duals [19]. The output of the dual theory is to find a well defined fermionic dual in order to make the field local and the fermionic theory covariant under Lorentz symmetries.…”

Exploiting new classes of mass-dimension one fermions

“…Quite recently, in [4,5], a new mathematical tool has been investigated, the so-called square root of 4×4 identity matrix, which provides a mechanism to define the expansion coefficients of spin one-half fermionic fields [4]. The given method allows us to construct new classes of fermionic fields, based on eigenvectors of a linearly independent set of re-arrangements of the Clifford matrices, which are, however, characterized for their being of mass-dimension one.…”