Bound states of the quasipotential equation for two spin-12particles in strongly coupled quantum electrodynamics

The bound states of two spin-$\frac{1}{2}$ particles in strongly coupled quantum electrodynamics are examined using a local quasipotential equation recently proposed by Todorov. Because of repulsive recoil effects displayed by the spatial part of the vector potential, complex energies do not appear for large $\alpha$ as with the static-limit equations, and very deep binding is obtained for $\alpha$ sufficiently large. No cutofs or charge distributions need to be introduced to obtain this result. The generalized ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ positronium system examined here appears to be confined to a thin spherical shell in this deep-binding limit.