Generalized Killing equations for spinning spaces and the role of Killing-Yano tensors

TL;DR

This paper explores generalized Killing equations in spinning spaces, showing solutions via Killing-Yano tensors, and discusses how constants of motion extend or differ from scalar cases due to spin variables.

Contribution

It introduces solutions to generalized Killing equations in spinning spaces using Killing-Yano tensors, highlighting new constants of motion related to spin variables.

Findings

Solutions expressed in terms of Killing-Yano tensors

Constants of motion extend scalar case results

New constants depend on Grassmann-valued spin variables

Abstract

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Solutions of these equations are expressed in terms of Killing-Yano tensors. In general the constants of motion can be seen as extensions of those from the scalar case or new ones depending on the Grassmann-valued spin variables.