Constrained BRST-BFV and BRST-BV Lagrangians for Half-Integer HS Fields on${{R}^{{1,d - 1}}}$

Abstract

Gauge invariant Lagrangian descriptions of half-integer higher-spin mixed-symmetric massless representations of the Poincare group with off-shell algebraic constraints are constructed within a metric-like formulation on the basis of a suggested constrained BRST approach. A gauge-invariant Fang–Fronsdal Lagrangian from the constrained BRST formulation are produced entirely in terms of the initial triple gamma-traceless spin-tensor field ${{\Psi }_{{{{{(\mu )}}_{n}}}}}$ with gamma-traceless gauge parameter. The triplet and quartet formulations are derived. The minimal (un)constrained BRST–BV actions for above formulations are obtained from proposed constrained BRST–BV approach.