Taub-NUT dynamics with a magnetic field

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.