Irreducible representations of the inhomogeneous Lorentz group with two-fold Wigner degeneracy

TL;DR

This paper explores how Elko spinors, with a two-fold Wigner degeneracy, can serve as expansion coefficients in quantum fields, evading Weinberg's no-go theorem and potentially modeling dark matter.

Contribution

It demonstrates that Elko spinors can be used in quantum fields by exploiting a unique degeneracy, challenging previous assumptions and expanding the class of viable dark matter candidates.

Findings

Elko spinors enable quantum field expansion without violating Weinberg's theorem.

The two-fold Wigner degeneracy leads to a consistent dark matter quantum field.

Elko's properties allow for unconventional representations of inversion symmetry.

Abstract

Not all complete set of spinors can be used as expansion coefficients of a quantum field. In fact, Steven Weinberg established the uniqueness of Dirac spinors for this purpose provided: (a) one paid due attention to the multiplicative phases for each of the spinors, and (b) one paired these to creation and annihilation operators in a specific manner. This is implicit in his implementation of the rotational symmetry for the spin half quantum field. Among the numerous complete set of spinors that are available to a physicist, Elko occupies a unique status that allows it to enter as expansion coefficients of a quantum field without violating Weinberg's no go theorem. How this paradigm changing claim arises is the primary subject of this communication. Weinberg's no go theorem is evaded by exploiting a uniquely special feature of Elko that allows us to introduce a doubling of the particle-antiparticle degrees of freedom from four to eight. Weinberg had dismissed this degeneracy on the ground that, "no examples are known of particles that furnish unconventional representations of inversions." Here we will find that this degeneracy, once envisioned by Eugene Wigner, in fact gives rise to a quantum field that has all the theoretical properties required of dark matter.