Supersymmetries and constants of motion in Taub-NUT spinning space

TL;DR

This paper reviews the motion of spinning particles in curved spaces, focusing on Taub-NUT space, and derives constants of motion using Killing-Yano tensors, providing an exact solution for certain trajectories.

Contribution

It introduces a method to express constants of motion for spinning particles in curved spaces using Killing-Yano tensors, applied specifically to Taub-NUT space.

Findings

Derived constants of motion in Taub-NUT space

Provided an exact solution for spinning particle trajectories

Connected Killing-Yano tensors to conserved quantities

Abstract

We review the geodesic motion of pseudo-classical spinning particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of Killing-Yano tensors. The general results are applied to the case of the four-dimensional Euclidean Taub-NUT spinning space. A simple exact solution, corresponding to trajectories lying on a cone, is given.