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.