Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background

TL;DR

This paper develops a gauge-invariant Lagrangian formulation for massive fermionic higher spin fields interacting with a constant electromagnetic background, using a BRST-based approach without off-shell constraints.

Contribution

It introduces a novel BRST-based method to construct gauge-invariant Lagrangians for massive higher spin fermionic fields in external electromagnetic fields, applicable in arbitrary dimensions.

Findings

Derived a gauge-invariant Lagrangian for spin 3/2 fermionic field

Established a general procedure for arbitrary spin fields

Maintained gauge invariance without off-shell constraints

Abstract

We consider massive half-integer higher spin fields coupled to an external constant electromagnetic field in flat space of an arbitrary dimension and construct a gauge invariant Lagrangian in the linear approximation in the external field. A procedure for finding the gauge-invariant Lagrangians is based on the BRST construction where no off-shell constraints on the fields and on the gauge parameters are imposed from the very beginning. As an example of the general procedure, we derive a gauge invariant Lagrangian for a massive fermionic field with spin 3/2 which contains a set of auxiliary fields and gauge symmetries.