Journal of High Energy Physics (Aug 2024)

Bertrand’s theorem and the double copy of relativistic field theories

  • Dijs de Neeling,
  • Diederik Roest,
  • Marcello Seri,
  • Holger Waalkens

DOI
https://doi.org/10.1007/JHEP08(2024)216
Journal volume & issue
Vol. 2024, no. 8
pp. 1 – 17

Abstract

Read online

Abstract Which relativistic field theories give rise to Kepler dynamics in the two-body problem? We consider a class of Hamiltonians that is the unique relativistic extension of the Kepler problem preserving its so(4) algebra, and have orbits related through time reparametrisation to orbits of the original Kepler problem. For three explicit examples, we give a natural interpretation in terms of spin-0,-1 and -2 interacting field theories in 5D. These are organically connected via the classical double copy, which therefore preserves maximal superintegrability.

Keywords