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.

36 pages, three figures

References in corpus (2)

• Time evolution in a geometric model of a particle
• Harmonic forms on ALF gravitational instantons

Cited by in corpus (7)

• Geodesic motion in Euclidean Schwarzschild geometry
• Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem
• Spectral Properties of Schwarzschild Instantons
• Wall Crossing from Dirac Zeromodes
• Harmonic Spinors on a Family of Einstein Manifolds
• Spectral Geometry of Nuts and Bolts
• Simulating Magnetic Monopole-Defect Dynamics