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 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.

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.

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We discuss a variational method for describing relativistic four-body systems within the Hamiltonian formalism of quantum field theory. The scalar Yukawa (or Wick–Cutkosky) model, in which scalar particles and antiparticles interact via a massive or massless scalar field, is used to illustrate the method. A Fock-space variational trial state is used to describe the stationary states of scalar quadronium (two particles and two antiparticles) interacting via one-quantum exchange and virtual annihilation pairwise interactions. Numerical results for the ground-state mass and approximate wave functions of quadronium are presented for various strengths of the coupling, for the massive and massless quantum exchange cases. PACS Nos.: 11.10Ef, 11.10St, 03.70+k, 03.65Pm