On Lagrangian formulations for arbitrary bosonic HS fields on Minkowski backgrounds

TL;DR

This paper reviews unconstrained Lagrangian formulations for arbitrary bosonic higher-spin fields in flat Minkowski space, using algebraic and BRST methods to derive gauge-invariant actions for massless and massive particles.

Contribution

It introduces a universal BRST-based approach to construct gauge-invariant Lagrangians for arbitrary bosonic higher-spin fields with Young tableau symmetries.

Findings

Derived explicit Lagrangians for massless and massive higher-spin bosonic fields.

Unified framework using Verma modules and oscillator realizations for HS symmetry algebra.

Reproduced gauge invariance with reducible gauge symmetries for arbitrary spins.

Abstract

We review the details of unconstrained Lagrangian formulations for Bose particles propagated on an arbitrary dimensional flat space-time and described by the unitary irreducible integer higher-spin representations of the Poincare group subject to Young tableaux $Y(s_1,...,s_k)$ with $k$ rows. The procedure is based on the construction of Verma modules and finding auxiliary oscillator realizations for the symplectic $sp(2k)$ algebra which encodes the second-class operator constraints subsystem in the HS symmetry algebra. Application of an universal BRST approach reproduces gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive bosonic fields of any spin with appropriate number of auxiliary fields.