An eight-component formalism is proposed for the relativistic two-fermion
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 which is symmetric in
the total cms energy. It
allows the extension of recent $\alpha^6$ recoil corrections to the positronium
case, and
implies new recoil corrections to
the fine and hyperfine structures and to the Bethe logarithm.
