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

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.