Effective one-body approach to the relativistic two-body problem

The relativistic two-body problem, much like the nonrelativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy, introduced some 30 years ago to compute relativistic corrections to the Balmer formula in quantum electrodynamics, is shown to wort; equally well for classical electromagnetic and gravitational interactions. The results for the gravitational two-body problem have more than an academic interest since they apply to the study of binary pulsars that provide precision tests for general relativity. They are compared with recent results derived by other methods.