The lagrangian description of representations of the Poincare group

TL;DR

This work develops a BRST-based Lagrangian framework for representing the Poincaré group by embedding irreducible and reducible higher-spin content into an auxiliary oscillator Fock space and employing dimensional reduction to manage second-class constraints. It constructs nilpotent BRST charges $Q$ and $\tilde{Q}$, yielding BRST-invariant Lagrangians that describe massive reducible spectra and massless irreducible spectra with two-row Young tableaux, with explicit realizations for simple cases such as antisymmetric 2-forms, mixed-symmetry tensors, and Weyl-tensor-like fields. Gauge invariances are shown to remove auxiliary components, leaving the desired irreducible content, and the formalism is extensible to arbitrary Poincaré representations. The discussion highlights pathways to include interactions and curved backgrounds (e.g., AdS), suggesting a systematic route toward consistent higher-spin dynamics within a BRST framework.

Abstract

The construction of lagrangians describing the various representations of the Poincare group is given in terms of the BRST approach.