Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimentions

TL;DR

This paper presents a gauge-invariant Lagrangian formulation for massive bosonic higher spin fields in arbitrary dimensions using the BRST approach, avoiding off-shell constraints and unifying multiple spins.

Contribution

It introduces a new BRST-based method for constructing gauge-invariant Lagrangians for massive higher spin fields without off-shell constraints, applicable in any dimension.

Findings

Derived Lagrangians for spin-1, spin-2, and spin-3 fields.

Constructed a unified Lagrangian for all massive bosonic fields.

Developed a general procedure for arbitrary spin in D dimensions.

Abstract

We develop the BRST approach to Lagrangian formulation for massive higher integer spin fields on a flat space-time of arbitrary dimension. General procedure of gauge invariant Lagrangian construction describing the dynamics of massive bosonic field with any spin is given. No off-shell constraints on the fields (like tracelessness) and the gauge parameters are imposed. The procedure is based on construction of new representation for the closed algebra generated by the constraints defining an irreducible massive bosonic representation of the Poincare group. We also construct Lagrangian describing propagation of all massive bosonic fields simultaneously. As an example of the general procedure, we derive the Lagrangians for spin-1, spin-2 and spin-3 fields containing total set of auxiliary fields and gauge symmetries of free massive bosonic higher spin field theory.