Taub-NUT Dynamics with a Magnetic Field

Abstract

We study classical and quantum dynamics on the Euclidean Taub-NUT geometry coupled to an abelian gauge field with self-dual curvature and show that, even though Taub-NUT has neither bounded orbits nor quantum bound states, the magnetic binding via the gauge field produces both. The conserved Runge-Lenz vector of Taub-NUT dynamics survives, in a modified form, in the gauged model and allows for an essentially algebraic computation of classical trajectories and energies of quantum bound states. We also compute scattering cross sections and find a surprising electric-magnetic duality. Finally, we exhibit the dynamical symmetry behind the conserved Runge-Lenz and angular momentum vectors in terms of a twistorial formulation of phase space.