Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields

TL;DR

This paper develops unconstrained local Lagrangians and field equations for higher-spin Bose fields with mixed symmetry, extending previous constrained formulations and identifying Weyl-like symmetries in flat space.

Contribution

It provides the first unconstrained metric-like Lagrangians for mixed symmetry higher-spin Bose fields, building on and extending Labastida's constrained framework.

Findings

Recovered Labastida's Lagrangians via Bianchi identities.

Extended to minimal unconstrained form with higher derivatives.

Identified classes invariant under Weyl-like symmetries.

Abstract

This is the first of two papers devoted to the local "metric-like" unconstrained Lagrangians and field equations for higher-spin gauge fields of mixed symmetry in flat space. Here we complete the previous constrained formulation of Labastida for Bose fields. We thus recover his Lagrangians via the Bianchi identities, before extending them to their "minimal" unconstrained form with higher derivatives of the compensator fields and to yet another, non-minimal, form with only two-derivative terms. We also identify classes of these systems that are invariant under Weyl-like symmetries.