[Paper Review] A Lorentz covariant local theory of fermions with mass dimension one

Dharam Vir Ahluwalia|arXiv (Cornell University)|Jan 13, 2016

Noncommutative and Quantum Gravity Theories3 citations

TL;DR

This paper presents a novel, local, and Lorentz-covariant quantum field theory for spin-1/2 fermions with mass dimension one, achieved through a redefined spinor dual that restores locality and symmetry. The key contribution is a consistent field formulation that resolves long-standing issues in mass-dimension-one fermionic theories by exploiting a subtle freedom in spinor duality definitions.

ABSTRACT

Here we present a local, Lorentz covariant, mass-dimension one fermionic quantum field of spin one half. The full restoration of locality and Lorentz symmetry comes about because of a subtle freedom that exists in defining the duals of spinors. In order that the new result is easily accessible we present an ab initio definition of the spin-one-half expansion coefficients and their main properties. This is followed by the construction of the new dual. We then use these results to present the mass-dimension one quantum field with the stated properties.

Motivation & Objective

• To construct a local and Lorentz-covariant quantum field theory for spin-1/2 fermions with mass dimension one.
• To resolve the longstanding challenge of restoring locality and Lorentz symmetry in mass-dimension-one fermionic theories.
• To provide a self-contained, ab initio definition of spin-1/2 expansion coefficients and their duals for clarity and accessibility.
• To establish a consistent field formulation that maintains fundamental symmetries while assigning mass dimension one to the fermion field.

Proposed method

• An ab initio construction of spin-1/2 expansion coefficients and their fundamental properties is developed from first principles.
• A new definition of the spinor dual is introduced, exploiting a subtle freedom in dual construction to restore Lorentz covariance.
• The new dual is used to define a consistent mass-dimension-one fermionic field Lagrangian that maintains locality.
• The full field theory is constructed using the new dual, ensuring manifest Lorentz invariance and local dynamics.
• The approach avoids non-locality and symmetry breaking by carefully defining spinor duals in a way that preserves covariance.

Experimental results

Research questions

• RQ1 How can a mass-dimension-one fermionic field be made locally Lorentz invariant?
• RQ2 What role does the choice of spinor dual play in restoring Lorentz symmetry in such theories?
• RQ3 Is it possible to construct a consistent quantum field theory for spin-1/2 fermions with mass dimension one without sacrificing locality?
• RQ4 What are the fundamental properties of expansion coefficients and duals in this new formulation?

Key findings

• A new, consistent definition of the spinor dual restores Lorentz covariance to a mass-dimension-one fermionic field.
• The resulting field theory is both local and Lorentz covariant, resolving a major obstacle in the field's development.
• The construction is self-contained and based on an ab initio definition of expansion coefficients and their duals.
• The theory maintains fundamental symmetries while assigning mass dimension one to the fermion field, a property previously thought incompatible with locality and covariance.