Evading Weinberg's no-go theorem to construct mass dimension one fermions: Constructing darkness

Abstract

Recent theoretical work reporting the construction of a new quantum field of spin one half fermions with mass dimension one requires that Weinberg's no go theorem must be evaded. Here we show how this comes about. The essence of the argument is to first define a quantum field with due care being taken in fixing the locality phases attached to each of the expansion coefficients. The second ingredient is to systematically construct the dual of the expansion coefficients to define the adjoint of the field. The Feynman-Dyson propagator constructed from the vacuum expectation value of the field and its adjoint then yields the mass dimensionality of the field. For a quantum field constructed from a complete set of eigenspinors of the charge conjugation operator, with locality phases judiciously chosen, the Feynman-Dyson propagator determines the mass dimension of the field to be one, rather than three halves. The Lorentz symmetry is preserved, locality anticommutators are satisfied, without violating fermionic statistics as needed for the spin one half field.

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

“…It is important to emphasize the physical content encoded in Eq. (6). As usual, it is still saying that under parity the creation operator at some point x is transformed into a creation operator at Px.…”

“…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).…”

Some remarks on dual helicity flag-dipole spinors

“…the reader is cautioned to do not naively neglect the relation φ ± R (0) = −φ ± L (0) when dealing antiparticles, as highlighted in [25,26]. An inspection of the helicity operator furnish…”

“…The aforementioned remark is a hint towards the canonical mass dimension related to the type-4 spinors, which allow us to assert that it is not 3/2, as conventionally was expected for fermions. Acting again with the Dirac operator γ µ p µ , in (25), it yields…”

Elko under spatial rotations

“…The effect of the rotation by 2π radians on the eigenspinors of the parity -that is, the Dirac spinors -is the same as on Weyl spinors. It is because for these spinors the right-and left-transforming components have the same helicity [1,2]. And the rotation induced phases, being same, factor out.…”