Geometric Lagrangians for massive higher-spin fields

TL;DR

This paper introduces geometric Lagrangians for massive higher-spin fields by extending massless gauge-invariant theories with quadratic polynomials, avoiding auxiliary fields and generalizing Fierz-Pauli mass terms.

Contribution

It proposes a novel class of gauge-invariant Lagrangians for massive higher-spin bosons and fermions using geometric methods without auxiliary fields.

Findings

Lagrangians are gauge invariant and geometric in nature.

Mass terms include all possible traces of the fields.

No auxiliary fields are required for the formulation.

Abstract

Lagrangians for massive, unconstrained, higher-spin bosons and fermions are proposed. The idea is to modify the geometric, gauge invariant Lagrangians describing the corresponding massless theories by the addition of suitable quadratic polynomials. These polynomials provide generalisations of the Fierz-Pauli mass term containing all possible traces of the basic field. No auxiliary fields are needed.