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

TL;DR

This paper demonstrates how to construct a spin one-half fermionic quantum field with mass dimension one by carefully defining the field, its dual, and locality phases, evading Weinberg's no-go theorem while preserving Lorentz symmetry and fermionic statistics.

Contribution

It provides a systematic method to construct mass dimension one fermions that evade Weinberg's no-go theorem, ensuring Lorentz invariance and proper fermionic behavior.

Findings

Constructed a quantum field with mass dimension one.

Maintained Lorentz symmetry and locality.

Ensured fermionic statistics are satisfied.

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 adjoint/dual 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 has mass dimension one. The Lorentz symmetry is preserved, locality anticommutators are satisfied, without violating fermionic statistics as needed for the spin one half field.