Gauge invariant Lagrangian construction for massive higher spin fermionic fields

TL;DR

This paper develops a gauge invariant Lagrangian framework for massive higher spin fermionic fields in any dimension, using BRST charge construction without initial off-shell constraints, and demonstrates its application to spin 3/2 fields.

Contribution

It introduces a novel, constraint-free, gauge invariant Lagrangian formulation for massive higher spin fermionic fields using BRST methods, applicable in arbitrary dimensions.

Findings

Constructed BRST charge for massive higher spin fermions.

Derived gauge invariant equations of motion without initial off-shell constraints.

Provided explicit Lagrangian for massive spin 3/2 field.

Abstract

We formulate a general gauge invariant Lagrangian construction describing the dynamics of massive higher spin fermionic fields in arbitrary dimensions. Treating the conditions determining the irreducible representations of Poincare group with given spin as the operator constraints in auxiliary Fock space, we built the BRST charge for the model under consideration and find the gauge invariant equations of motion in terms of vectors and operators in the Fock space. It is shown that like in massless case hep-th/0410215, the massive fermionic higher spin field models are the reducible gauge theories and the order of reducibility grows with the value of spin. In compare with all previous approaches, no off-shell constraints on the fields and the gauge parameters are imposed from the very beginning, all correct constraints emerge automatically as the consequences of the equations of motion. As an example, we derive a gauge invariant Lagrangian for massive spin 3/2 field.