Dynamical symmetries of generalized Taub-NUT and multi-center metrics

TL;DR

This paper explores hidden symmetries in generalized Taub-NUT and multi-center metrics, revealing conserved quantities like Runge-Lenz types and identifying new charges in non-Abelian gauge field systems.

Contribution

It systematically analyzes symmetries using Killing tensors, constructs conserved quantities for generalized metrics, and uncovers new conserved charges in non-Abelian gauge field models.

Findings

Kepler-type symmetries in generalized Taub-NUT metrics

Existence of a conserved Runge-Lenz scalar in two-center metrics

Discovery of a new conserved charge in non-Abelian gauge systems

Abstract

Hidden symmetries of generalized Kaluza-Klein-type metrics are studied using van Holten's systematic analysis \cite{vH} based on Killing tensors. Applied to generalized Taub-NUT metrics, Kepler-type symmetries with associated Runge-Lenz-type conserved quantities are constructed. In the multicenter case, the subclass of two-center metrics gives rise to a conserved Runge-Lenz-type scalar, while no Kepler-type constant of the motion does exist for non aligned $(N\geq3)$-centers. We also investigated the diatomic molecule system of Wilczek et al. where "truly" non-Abelian gauge fields mimicking monopole-like fields arised. From the latter system we deduced a new conserved charge.