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 $J^{\mathrm{PC}}=O^{-+}$. 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 $\gamma -\gamma$ scattering channel. Consequences for photon-photon scattering experiments are discussed briefly.

• Received 11 March 1991

DOI:https://doi.org/10.1103/PhysRevD.45.675