  We consider particle-antiparticle bound states in the scalar Yukawa
(Wick-Cutkosky) model. The variational method in the Hamiltonian formalism of
quantum field theory is employed. A reformulation of the model is studied, in
which covariant Green's functions are used to solve for the mediating field in
terms of the particle fields. A simple Fock-state variational ansatz is used to
derive a relativistic equation for the particle-antiparticle states. This
equation contains one-quantum-exchange and virtual-annihilation interactions.
  It is shown that analytic solutions of this equation can be obtained for the
simplified case where only the virtual annihilation interaction is retained.
More generally, numerical and perturbative solutions of the equation are
obtained for the massive and massless-exchange cases. We compare our results
with various Bethe-Salpeter-based calculations.

Nuclear Theory;High Energy Physics - Phenomenology