Spin raising and lowering operators for Rarita-Schwinger fields

TL;DR

This paper develops spin raising and lowering operators for massless Rarita-Schwinger fields using twistor spinors, highlighting the necessity of Ricci-flat backgrounds and deriving symmetry operators for these fields.

Contribution

It introduces a novel method to construct solutions and symmetry operators for Rarita-Schwinger fields from twistor spinors, emphasizing Ricci-flat backgrounds.

Findings

Solutions derived from source-free Maxwell fields and twistor spinors.

Construction requires Ricci-flat backgrounds due to gauge invariance.

Identifies constraints and symmetry operators for Rarita-Schwinger fields.

Abstract

Spin raising and lowering operators for massless field equations constructed from twistor spinors are considered. Solutions of the spin-$\frac{3}{2}$ massless Rarita-Schwinger equation from source-free Maxwell fields and twistor spinors are constructed. It is shown that this construction requires Ricci-flat backgrounds due to the gauge invariance of the massless Rarita-Schwinger equation. Constraints to construct spin raising and lowering operators for Rarita-Schwinger fields are found. Symmetry operators for Rarita-Schwinger fields via twistor spinors are obtained.