Elko in 1+1 dimensions

TL;DR

This paper investigates the Lorentz symmetry violation in Elko quantum fields of various spins, revealing inherent non-locality and preferred directions, with implications for dark matter models.

Contribution

It demonstrates that Elko quantum fields inherently violate Lorentz symmetry and explores their kinematic properties across different spins.

Findings

Elko fields violate Lorentz symmetry from first principles.

Elko exhibits non-locality with a preferred direction.

The kinematics of Elko fields are characterized for any spin.

Abstract

The quantum field operator for spin-half Elko describes a massive self-interacting fermionic dark matter candidate of mass dimension one. It has been shown that the theory has a built-in violation of the Lorentz symmetry and a well-defined element of non-locality in the form of a preferred direction. This note shows that quantum field operators constructed using spin-half and higher-spin Elko violate Lorentz symmetry from first principle. Subsequently, we study the kinematics of Elko and its quantum field operator for any spin along the preferred direction.