Self-interacting mass-dimension one fields for any spin

TL;DR

This paper extends the concept of mass-dimension one fermionic fields to higher spins using Elko eigenspinors, exploring their properties, equations, and Lorentz-violating features, with implications for renormalizable interactions.

Contribution

It generalizes the construction of mass-dimension one fields to arbitrary spin, analyzing their kinematics, propagators, Hamiltonians, and Lorentz-violating characteristics.

Findings

Fields satisfy higher-spin Klein-Gordon equations, not Dirac.

All fields have mass-dimension one, enabling renormalizable self-interactions.

Lorentz violation characterized by non-covariant terms in spin-sums.

Abstract

According to Ahluwalia and Grumiller, massive spin-half fields of mass-dimension one can be constructed using the eigenspinors of the charge-conjugation operator (Elko) as expansion coefficients. In this paper, we generalize their result by constructing quantum fields from higher-spin Elko. The kinematics of these fields are thoroughly investigated. Starting with the field operators, their propagators and Hamiltonians are derived. These fields satisfy the higher-spin generalization of the Klein-Gordon but not the Dirac equation. Independent of the spin, they are all of mass-dimension one and are thus endowed with renormalizable self-interactions. These fields violate Lorentz symmetry. The violation can be characterized by a non Lorentz-covariant term that appears in the Elko spin-sums. This term provides a decomposition of the generalized higher-spin Dirac operator in the momentum space thus suggesting a possible connection between the mass-dimension one fields and the Lorentz-invariant fields.