We study the QED bound-state problem in a light-front hamiltonian approach.
Starting with a bare cutoff QED Hamiltonian, HB, with matrix elements
between free states of drastically different energies removed, we perform a
similarity transformation that removes the matrix elements between free states
with energy differences between the bare cutoff, Λ, and effective
cutoff, \lam (\lam < \Lam). This generates effective interactions in the
renormalized Hamiltonian, HR. These effective interactions are derived
to order α in this work, with α≪1. HR is renormalized
by requiring it to satisfy coupling coherence. A nonrelativistic limit of the
theory is taken, and the resulting Hamiltonian is studied using bound-state
perturbation theory (BSPT). The effective cutoff, \lam^2, is fixed, and the
limit, 0 \longleftarrow m^2 \alpha^2\ll \lam^2 \ll m^2 \alpha \longrightarrow
\infty, is taken. This upper bound on \lam^2 places the effects of
low-energy (energy transfer below \lam) emission in the effective
interactions in the ∣ee> sector. This lower bound on \lam^2
insures that the nonperturbative scale of interest is not removed by the
similarity transformation. As an explicit example of the general formalism
introduced, we show that the Hamiltonian renormalized to O(α) reproduces
the exact spectrum of spin splittings, with degeneracies dictated by rotational
symmetry, for the ground state through O(α4). The entire calculation is
performed analytically, and gives the well known singlet-triplet ground state
spin splitting of positronium, 7/6α2Ryd. We discuss remaining
corrections other than the spin splittings and how they can be treated in
calculating the spectrum with higher precision.Comment: 46 pages, latex, 3 Postscript figures included, section on remaining
corrections added, title changed, error in older version corrected, cutoff
placed in a windo