Unfolded Fierz-Pauli Equations in Three-Dimensional Asymptotically Flat Spacetimes

TL;DR

This paper develops a covariant formulation of Fierz-Pauli equations for massive higher-spin fields in three-dimensional asymptotically flat spacetimes using algebraic quotient methods, revealing an infinite tower of decoupled fields.

Contribution

It introduces an unfolded, covariant approach to higher-spin Fierz-Pauli equations in 3D flat spacetimes via algebraic quotients, extending the understanding of higher-spin field equations.

Findings

Formulation of covariant Fierz-Pauli equations using algebraic quotients.

Decoupling of fundamental fields in the unfolded system.

Presence of infinitely many copies of each spin field in the non-truncated case.

Abstract

We utilise a quotient of the universal enveloping algebra of the Poincar\'e algebra in three spacetime dimensions, on which we formulate a covariant constancy condition. The equations so obtained contain the Fierz-Pauli equations for non-interacting, massive higher-spin fields, and can thus be regarded as an unfolding of the Fierz-Pauli system. All fundamental fields completely decouple from each other. In the non-truncated case, the field content includes infinitely many copies of each field at fixed spin.