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A Hamiltonian variational method is used in quantum field theory to describe photon-photon scattering in quantum electrodynamics (QED) at energies where the cross section is dominated by the formation of positronium states of symmetry JPC=O^-+. It is shown how the originally homogeneous eigen-value equation for the positronium bound states is augmented by an inhomogeneity due to the coupling to the two-photon sector. Thus our calculation reproduces the well-known result that QED has a continuous spectrum at all energies and that the positronium bound states appear as resonances in the γ-γ scattering channel. Consequences for photon-photon scattering experiments are discussed briefly.
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Darewych et al. (1992) studied this question.
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