Symmetry of massive Rarita-Schwinger fields

TL;DR

This paper develops a comprehensive framework for massive Rarita-Schwinger fields, revealing a previously underexplored symmetry that leads to conserved currents and has potential implications in high-energy physics and supergravity.

Contribution

It introduces a general Lagrangian and propagator for vector-spinor fields in arbitrary dimensions, and explores the consequences of a novel point transformation symmetry.

Findings

Invariance of physical observables under point transformations.

Existence of a conserved vector current and charge.

Potential applications in hadron physics and supergravity.

Abstract

We derive the general lagrangian and propagator for a vector-spinor field in $d$-dimensions and show that the physical observables are invariant under the so-called point transformation symmetry. Until now the symmetry has not been exploited in any non-trival way, presumably because it is not an invariance of the classical action nor is it a gauge symmetry. Nevertheless, we develop a technique for exploring the consequences of the symmetry leading to a conserved vector current and charge. The current and charge are identically zero in the free field case and only contribute in a background such as a electromagnetic or gravitational field. The current can couple spin-3/2 fields to vector and scalar fields and may have important consequences in intermediate energy hadron physics as well as linearized supergravity. The consistency problem which plagues higher spin field theories is then discussed and and some ideas regarding the possiblity of solutions are presented.