O(4,2) dynamical symmetry of the Kaluza-Klein monopole

Hidden symmetries of dynamics in classical and quantum physics

“…From eqs. (162) and (165) it is possible to generate Killing-Yano and, respectively, closed conformal KillingYano tensors onM when f is Killing-Yano and, respectively closed conformal Killing-Yano on M. In particular this gives new examples of Lorentzian metrics with conformal Killing-Yano tensors by lifting known conformal Killing-Yano tensors in Riemannian signature, for example when M is the Kerr-NUT-(A)dS metric or the Taub-NUT metric (Baleanu and Codoban, 1999;Cordani et al, 1988;Gibbons and Ruback, 1987;Vaman and Visinescu, 1998;Visinescu, 2000).…”

“…Gibbons and Manton showed that this metric admits a conserved vector of the Runge-Lenz type (Gibbons and Manton, 1986), Feher and Horvathy studied its dynamical symmetries, showing that together with angular momentum it generates an O(4) or O(1, 3) algebra analogous to that of the Kepler problem, in particular allowing to calculate the bound-state spectrum and the scattering cross section (Fehér and Horváthy, 1987a,b). More generic Kepler-type dynamical symmetries applied to the study of monopole interactions have been considered in (Cordani et al, 1988(Cordani et al, , 1990Fehér and Horváthy, 1988). The study of the Dirac equation in Taub-NUT space has been considered for example in (Comtet and Horváthy, 1995;, as well as supersymmetry of monopoles and vortices (Horváthy, 2006).…”

Quantum integrability of quadratic Killing tensors

“…These conditions insure that the metric (2.49) is Ricci-flat. For some special potentials V (y), the geodesic flow is integrable as shown in [20,13,35]. The four conserved quantities in involution are given by…”

Motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime and analytical solutions

“…In fact, the geodesic equations have been investigated in the spacetimes with Taub-NUT charge in the works [13,14,15,16,17]. Especially in [13,14] dynamical symmetries of the geodesic motion in the spacetime with NUT parameter (which describes four dimensional Bogomol'nyi-Prasad-Sommerfield (BPS) monopoles and five dimensional Kaluza-Klein monopoles respectively) have been illustrated. In this sense, our aim is to obtain the analytical solutions of the equations of motion for a charged test particle in the background of Kerr-NewmanTaub-NUT spacetime and examine the effect of the NUT parameter and the charge of the test particle.…”