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- W2079666112 abstract "We study the QED bound-state problem 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, $Lambda$, and effective cutoff, $lam$ ($lam < Lam$). This generates effective interactions in the renormalized Hamiltonian, $H_{_{R}}$. These effective interactions are derived to order $alpha$ in this work, with $alpha ll 1$. $H_{_{R}}$ 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, $0 longleftarrow m^2 alpha^2ll lam^2 ll m^2 alpha longrightarrow infty$, 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 $| e {overline e} > $ 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 $O(alpha)$ reproduces the exact spectrum of spin splittings, with degeneracies dictated by rotational symmetry, for the ground state through $O(alpha^4)$. The entire calculation is performed analytically, and gives the well known singlet-triplet ground state spin splitting of positronium, $7/6 alpha^2 Ryd$. We discuss remaining corrections other than the spin splittings and how they can be treated in calculating the spectrum with higher precision." @default.
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- W2079666112 date "1997-05-15" @default.
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- W2079666112 title "Analytic treatment of positronium spin splittings in light-front QED" @default.
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- W2079666112 doi "https://doi.org/10.1103/physrevd.55.6561" @default.
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