1/c expansion of bound-state energies in QED

A new method for calculating bound-state energies in quantum electrodynamics is proposed. It starts from a non-relativistic Schrödinger equation as a zeroth approximation and treats the relativistic corrections by a systematic expansion. The result is expressed as a sum over Feynman-like graphs. No relativistic bound-state equations are used. Only the case of positronium is considered explicitly, but the method generalizes easily to other cases.