Massless Poincare modules and gauge invariant equations

TL;DR

This paper develops a gauge-invariant framework for free higher spin fields with mixed symmetry on Minkowski space, connecting Poincare modules to Lagrangian theories and reproducing known formulations.

Contribution

It introduces a method to construct gauge theories from indecomposable Poincare modules, unifying various descriptions of mixed-symmetry higher spin fields.

Findings

Constructed gauge theories from Poincare modules.

Reproduced Labastida and unfolded formulations.

Confirmed unitarity and irreducibility in momentum space.

Abstract

Starting with an indecomposable Poincare module M_0 induced from a given irreducible Lorentz module we construct a free Poincare invariant gauge theory defined on the Minkowski space. The space of its gauge inequivalent solutions coincides with (in general, is closely related to) the starting point module M_0. We show that for a class of indecomposable Poincare modules the resulting theory is a Lagrangian gauge theory of the mixed-symmetry higher spin fields. The procedure is based on constructing the parent formulation of the theory. The Labastida formulation and the unfolded description of the mixed symmetry fields are reproduced through the appropriate reductions of the parent formulation. As an independent check we show that in the momentum representation the solutions form a unitary irreducible Poincare module determined by the respective module of the Wigner little group.