Newton's Off-Center Circular Orbits and the Magnetic Monopole

Abstract

Introducing a radially dependent magnetic field into Newton's off-center circular orbits potential to preserve the 𝐸 = 0 dynamical symmetry leads to a unique choice of field that can be identified as the inclusion of a magnetic monopole in the inverse stereographically projected problem. One also finds a phenomenological correspondence with that of the linearly damped Kepler model. The presence of the monopole field deforms the symmetry algebra by a central extension, and the quantum mechanical version of this algebra reveals several zero modes equal to those counted using the index theorem of elliptic operators.