BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields

TL;DR

This paper develops a BRST-based method to construct gauge-invariant Lagrangians for mixed-symmetry fermionic higher-spin fields in flat space, avoiding off-shell constraints and handling both massless and massive cases.

Contribution

It introduces a universal BRST approach for formulating Lagrangians of mixed-symmetry fermionic higher-spin fields without off-shell constraints, applicable to any spin and mass.

Findings

Constructed gauge-invariant Lagrangians for specific mixed-symmetry fermionic fields.

Demonstrated the method's applicability to massless and massive fields.

Provided explicit examples with detailed auxiliary fields and gauge symmetries.

Abstract

We construct a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a description of fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find auxiliary representations of the constraint subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincare-group representation. To illustrate the general construction, we obtain a Lagrangian description of fermionic fields with generalized spin (3/2,1/2) and (3/2,3/2) on a flat background containing the complete set of auxiliary fields and gauge symmetries.