Bound and resonant relativistic two-particle states in scalar quantum field theory

We derive relativistic particle-antiparticle wave equations for scalar particles, φ and Φ, interacting via a massive or massless scalar field, χ (the Wick-Cutkosky model). The variational method, within the Hamiltonian formalism of quantum field theory is used to derive equations with and without coupling of this quasi-bound φΦ system to the χχ decay channel. Bound-state energies in the massless case are compared with the ladder Bethe-Salpeter and light-cone results. In the case of coupling to the decay channel, the quasi-bound φΦ states are seen to arise as resonances in the χΧ scattering cross section. Numerical results are presented for the massive and massless χ case. (author)