Effect of virtual pairs for relativistic bound-state problems

We use the variational method within the Hamiltonian formalism of quantum field theory to derive relativistic two-, (four)-, and (six)-body wave equations for scalar particles interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Fock-space variational trial states [2+(4)+(6)] are used to derive the relativistic two-body system. The equations are shown to have the Schroedinger nonrelativistic limit, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. The results show that the inclusion of virtual pairs has a large effect for the binding energy of the system at strong coupling. In the case of the discovery of a scalar Higgs particle in upcoming experiments, we may apply the present results to real, physical systems.