The Theory of Local Mass Dimension One Fermions of Spin One Half

Abstract

Abstract. About a decade ago the present author in collaboration with Daniel Grumiller presented an 'unexpected theoretical discovery' of spin one-half fermions with mass dimension one [1,2]. In the decade that followed a significant number of groups explored intriguing mathematical and physical properties of the new construct. However, the formalism suffered from two troubling features, that of non-locality and a subtle violation of Lorentz symmetry. Here, we trace the origin of both of these issues to a hidden freedom in the definition of duals of spinors and the associated field adjoints. In the process, for the first time, we provide a quantum theory of spin one-half fermions that is free from all the mentioned issues. The interactions of the new fermions are restricted to dimension-four quartic self interaction, and also to a dimensionfour coupling with the Higgs. A generalised Yukawa coupling of the new fermions with neutrinos provides an hitherto unsuspected source of lepton-number violation. The new fermions thus present a first-principle dark matter partner to Dirac fermions of the standard model of high energy physics with contrasting mass dimensions -that of three halves for the latter versus one of the former without mutating the statistics from fermionic to bosonic.

Massive spin-one-half one-particle states for the mass-dimension-one fermions

“…A direct computation of reflections on the expansion coefficients is built in Ref. [5] evincing that such spinors give rise to Wigner class 3 particles. In fact, Ref.…”

“…In fact, Ref. [5] shows the existence of four different spinors whose associated particles belongs to H D . In this regard P , acting on the alluded particle states, perform an endomorphism of H D on itself.…”

“…We shall finalize by given a non rigorous attempt to interpret the label h here used to lift the degeneracy in question. As worked out, the Poincaré invariance of the mass dimension one spinor is attained by means of a judicious dual spinor theory [5,6]. Up to our knowledge, the spinors used to built the theory, the correct dual appreciation apart, may carry symmetries from an eight dimension subalgebra of the Poincaré algebra (see [10] for this formulation).…”

Constraints on mapping the Lounesto’s classes

“…However, this only happens for eigenspinors of parity operator. For the eigenspinors of charge conjugation operator, the phases factor must be ϑ 1 = 0 and ϑ 2 = π [9]. Thus, this judicious combination of ϑ 1 and ϑ 2 ensure locality for field -further details can be found in [8].…”

Some remarks on dual helicity flag-dipole spinors

“…where the parameters α and β are constant phases to be further determined. Note that the (0, 1/2) and (1/2, 0) representation spaces are now connected by the Wigner Time-Reversal operator, Θ, similarly as Elko do [27]. Taking advantage of the last above feature and then taking a rest frame spinor to a momentum arbitrary referential, using the boost operator presented in (7), it follows…”