Perihelion Precession in the Special Relativistic Two-Body Problem

@article{Trump1998PerihelionPI,
  title={Perihelion Precession in the Special Relativistic Two-Body Problem},
  author={M. A. Trump and William C. Schieve},
  journal={Foundations of Physics},
  year={1998},
  volume={28},
  pages={1407-1416}
}
The classical two-body system with Lorentz-invariant Coulomb work function V = -k/ρ is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stückelberg. Particular solutions for the reduced motion are obtained which correspond to bound attractive, unbound attractive, and repulsive scattering motion. A lack of perihelion precession is found in the bound attractive orbit, and the semiclassical hydrogen spectrum subsequently contains no fine structure corrections. It is… 

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