Generalized Killing equations and Taub-NUT spinning space

TL;DR

This paper explores the generalized Killing equations for spinning particles, revealing solutions via Killing-Yano tensors, and applies these findings to the four-dimensional Euclidean Taub-NUT manifold to deepen understanding of symmetries in spinning space.

Contribution

It introduces solutions to generalized Killing equations using Killing-Yano tensors and applies them specifically to the Taub-NUT manifold, extending symmetry analysis in spinning particle configuration spaces.

Findings

Solutions expressed in terms of Killing-Yano tensors

Application to four-dimensional Euclidean Taub-NUT manifold

Enhanced understanding of symmetries in spinning space

Abstract

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Simple solutions of the homogeneous part of these equations are expressed in terms of Killing-Yano tensors. The general results are applied to the case of the four-dimensional euclidean Taub-NUT manifold.