Taub-NUT Dynamics with a Magnetic Field

TL;DR

This paper explores how a magnetic field influences classical and quantum dynamics on the Euclidean Taub-NUT space, revealing bound states, conserved quantities, and dualities not present without the magnetic field.

Contribution

It demonstrates that magnetic coupling induces bound states and modifies conserved quantities like the Runge-Lenz vector in Taub-NUT space, providing algebraic methods for trajectory and energy calculations.

Findings

Magnetic field induces bound states in Taub-NUT dynamics.

Conserved Runge-Lenz vector persists in a modified form.

Discovery of electric-magnetic duality in scattering cross sections.

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.