BRST-BFV Lagrangian Formulations for Higher Spin Fields subject to two-column Young Tableaux

TL;DR

This paper develops a BRST-BFV Lagrangian framework for describing higher-spin bosonic fields with two-column Young tableaux, enabling gauge-invariant formulations for massless and massive mixed-antisymmetric fields in any dimension.

Contribution

It introduces a novel BRST-BFV approach using auxiliary Fock space and oscillator realizations to construct gauge-invariant Lagrangians for higher-spin fields with two-column Young tableaux.

Findings

Constructed gauge-invariant Lagrangians for higher-spin fields

Derived reducible gauge symmetries for mixed-antisymmetric fields

Provided a systematic method for arbitrary dimensional Minkowski space

Abstract

The details of Lagrangian description of irreducible integer higher-spin representations of the Poincare group with an Young tableaux $Y[\hat{s}_1,\hat{s}_2]$ having $2$ columns are considered for Bose particles propagated on an arbitrary dimensional Minkowski space-time. The procedure is based, first, on using of an auxiliary Fock space generated by Fermi oscillators (antisymmetric basis), second, on construction of the Verma module and finding auxiliary oscillator realization for $sl(2)\oplus sl(2)$ algebra which encodes the second-class operator constraints subsystem in the HS symmetry superalgebra. Application of an BRST-BFV receipt permits to reproduce gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive mixed-antisymmetric bosonic fields of any spin with appropriate number of gauge and Stueckelberg fields. The general prescription possesses by the possibility to derive constrained Lagrangians with only BRST-invariant extended algebraic constraints which describes the Poincare group irreducible representations in terms of mixed-antisymmetric tensor fields with 2 group indices.