Conformal and gauge invariant spin-2 field equations

TL;DR

This paper derives conformal and gauge invariant equations for a fundamental spin-2 field in de Sitter space, revealing that interpreting the field as a 1-form valued in the translation group algebra achieves both invariance properties.

Contribution

It introduces a novel approach using Casimir operators to formulate conformal invariant equations for spin-2 fields, emphasizing the importance of field interpretation.

Findings

Conformal invariance is achieved only when the spin-2 field is a 1-form in the translation algebra.

Gauge invariance is compatible with conformal invariance under this interpretation.

The approach clarifies the structure of spin-2 fields in de Sitter space.

Abstract

Using an approach based on the Casimir operators of the de Sitter group, the conformal invariant equations for a fundamental spin-2 field are obtained, and their consistency discussed. It is shown that, only when the spin-2 field is interpreted as a 1-form assuming values in the Lie algebra of the translation group, rather than a symmetric second-rank tensor, the field equation is both conformal and gauge invariant.