Bertran\v{d}s Theorem and the Double Copy of Relativistic Field Theories

TL;DR

This paper explores how certain relativistic field theories, connected through the classical double copy, can produce Kepler-like dynamics in the two-body problem while preserving superintegrability.

Contribution

It identifies a class of relativistic Hamiltonians extending Kepler dynamics that maintain so(4) symmetry and demonstrates their relation via the classical double copy across different spin theories.

Findings

Kepler dynamics extended to relativistic Hamiltonians preserving so(4)

Explicit examples for spin-0, -1, and -2 theories in 5D

Double copy preserves maximal superintegrability

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.