Teleparallel origin of the Fierz picture for spin-2 particle

TL;DR

This paper introduces a teleparallel gravity-based framework for describing spin-2 particles, clarifying the structure of the Fierz tensor, gauge symmetry origin, and deriving the Einstein operator, with considerations for curved spacetime consistency.

Contribution

It establishes a natural teleparallel approach to the Fierz representation of spin-2 particles, linking it to fundamental teleparallel identities and gauge symmetry.

Findings

Unique structure of the Fierz tensor from teleparallel theory

Origin of gauge symmetry explained through teleparallel identity

Linearized Einstein operator derived from teleparallel gravity

Abstract

A new approach to the description of spin-2 particle in flat and curved spacetime is developed on the basis of the teleparallel gravity theory. We show that such an approach is in fact a true and natural framework for the Fierz representation proposed recently by Novello and Neves. More specifically, we demonstrate how the teleparallel theory fixes uniquely the structure of the Fierz tensor, discover the transparent origin of the gauge symmetry of the spin 2 model, and derive the linearized Einstein operator from the fundamental identity of the teleparallel gravity. In order to cope with the consistency problem on the curved spacetime, similarly to the usual Riemannian approach, one needs to include the non-minimal (torsion dependent) coupling terms.