An eight-component formalism is proposed for the relativistic two-ferm
ion problem. In QED it extends the applicability of the Dirac equation
with hyperfine interaction to the positronium case. The use of exact
relativistic two-body kinematics entails a CP-invariant spectrum that
is symmetric in the total center-of-mass system energy. it allows the
extension of recent alpha(6) recoil corrections to the positronium cas
e End implies recoil corrections to the fine and hyperfine structures
and to the Bethe logarithm.