  Modified similarity renormalization (MSR) of Hamiltonians is proposed, that
performes by means of flow equations the similarity transformation of
Hamiltonian in the particle number space. This enables to renormalize in the
energy space the field theoretical Hamiltonian and makes possible to work in a
severe trancated Fock space for the renormalized Hamiltonian.
  Original works of Wegner in solid state physics has served us as the guiding
principle in constructing the MSR scheme.
  The renormalized to the second order effective $QED_{3+1}$ Hamiltonian on the
light front is obtained. This Hamiltonian reproduces in $|e\bar{e}>$ sector the
standard singlet-triplet splitting of positronium and recorves rotational
symmetry of the canonical theory. The lowest and next-to-lowest energy states
of positronium are almost independent on the cutoff when in both cases the
'same' (state and sector independent) counterterms are included.
  The electron (photon) mass counterterms are IR (collinear) finite if all
diagrams to the second order, arising from the flow equations and
normal-ordering Hamiltonian, are taken into account, and vary with UV cutoff in
accordance with $1$-loop renormalization group equations.
  Both approximations of perturbation theory and Fock space trancation are
under the control and can be improved systematically within the proposed
renormalization scheme.
