Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 099, 10 pages      arXiv:2307.15222      https://doi.org/10.3842/SIGMA.2023.099

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

Dipesh Bhandari a and Michael Crescimanno b
a) Department of Physics and Astronomy, Texas A&M University-Commerce, TX, 75429, USA
b) Department of Physics and Astronomy, Youngstown State University, Youngstown, OH, 44555, USA

Received July 31, 2023; in final form December 08, 2023; Published online December 17, 2023

Abstract
Introducing a radially dependent magnetic field into Newton's off-center circular orbits potential so as 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 finds also 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 a number of zero modes equal to that counted using the index theorem of elliptic operators.

Key words: integrals of motion; magnetic monopole; zero modes.

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