Nonperturbative QED: An analytical treatment on the light front

We study positronium’s fine structure in a light-front hamiltonian approach. Starting with a bare cutoff QED hamiltonian, H B , 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 final cutoff, λ (λ < Λ). This generates effective interactions in the renormalized hamiltonian, H R . These effective interactions are derived to order α in this work, with α ≪ 1. H R is renormalized by requiring it to satisfy coupling coherence conditions. A nonrelativistic limit of the theory is taken with λ ≪ m, and the resulting hamiltonian is studied using bound state perturbation theory (BSPT). The similarity transformation we use is unitary, and the nonperturbative spectrum is independent of λ. However, H R is derived perturbatively to a finite order in e, therefore its spectrum depends on λ at some order in α. We show that the second-order H R has a spectrum that is independent of λ to order α for positronium. The singlet-triplet ground state mass splitting of positronium to order α, with degeneracies dictated by rotational symmetry, is shown to arise from the second order H R . The entire calculation is performed analytically and the well known result of