On quantum numbers for Rarita-Schwinger fields

TL;DR

This paper classifies first order symmetry operators commuting with the Rarita-Schwinger operator in various dimensions, revealing new connections with Killing-Yano tensors and extending previous four-dimensional results.

Contribution

It provides a comprehensive classification of first order commuting operators for Rarita-Schwinger fields, including their construction from Killing-Yano tensors in arbitrary dimensions.

Findings

Certain first order operators commute with the Rarita-Schwinger operator.

Construction of commuting operators from Killing-Yano tensors.

Extension of four-dimensional results to higher dimensions.

Abstract

We consider first order linear operators commuting with the operator appearing in the linearized equation of motion of Rarita-Schwinger fields which comes directly from the action. First we consider a simplified operator giving an equation equivalent to the original equation, and classify first order operators commuting with it in four dimensions. In general such operators are symmetry operators of the original operator, but we find that some of them commute with it. We extend this result in four dimensions to arbitrary dimensions and give first order commuting operators constructed of odd rank Killing-Yano and even rank closed conformal Killing-Yano tensors with additional conditions.