  The method of flow equations is applied to QED on the light front. Requiring
that the particle number conserving terms in the Hamiltonian are considered to
be diagonal and the other terms off-diagonal an effective Hamiltonian is
obtained which reduces the positronium problem to a two-particle problem, since
the particle number violating contributions are eliminated.
  Using an effective electron-positron Hamiltonian, obtained in the second
order in coupling, we analyze the positronium bound state problem analytically
and numerically. The results obtained for Bohr spectrum and hyperfine splitting
coincide to a high accuracy with experimental values. The rotational
invariance, that is not manifest symmetry on the light-front, is recovered for
positronium mass spectrum.
  Except for the longitudinal infrared divergences, that are special for the
light-front gauge calculations, no infrared divergences appear. The ultraviolet
renormalization in the second order in coupling constant is performed
simultaneously. To preserve boost invariance we take into account the diagrams
arising from the normal ordering of instantaneous interactions. Using flow
equations and coupling coherence we obtain the counterterms for electron and
photon masses, which are free from longitudinal infrared divergences.
