We use the Hamiltonian formalism of quantum field theory and the variational basis-state method to derive relativistic coupled-state wave equations for scalar particles interacting via a massive or massless mediating scalar field (the scalar Yukawa model). A variational trial state comprised of two and four Fockspace states is used to derive coupled wave equations for a relativistic two (and four) body system. Approximate, variational two-body ground-state solutions of the relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields. The results show that the inclusion of virtual pairs has a large effect on the two-body binding energy at strong coupling. A comparison of the two-body binding energies with other calculations is presented.
We use the variational method within the Hamiltonian formalism of QFT to derive relativistic two-, three- and four-body wave equations for scalar particles interacting via a massive or massless mediating scalar field (the scalar Yukawa model). The Lagrangian of the theory is reformulated by using Green's functions to express the mediating field in terms of the particle fields. The QFT is then constructed from the resulting reformulated Hamiltonian. Simple Fock-space variational trial states are used to derive relativistic two-, three- and four-body equations. The equations are shown to have the Schrödinger non-relativistic 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. Ground-state solutions of the relativistic equations are obtained approximately for various strengths of coupling, for both massive and massless mediating fields, and a comparison of the two-, three- and four-particle binding energies is presented.
The variational method in a reformulated Hamiltonian formalism of quantum electrodynamics is used to derive relativistic wave equations for a system consisting of n fermions and antifermions. Simple Fock-space variational trial states are used to obtain the relativistic n-body equations. The derived kernels of these equations ͑i.e., momentum-space relativistic potentials͒ include one-photon exchange and virtual annihilation interactions. The equations are shown to have the Schrödinger nonrelativistic limit. Application to the particular cases of positronium ͑Ps͒, positronium negative ion ͑Ps − ͒, and positronium molecule ͑Ps 2 , e − e + e − e + ͒ are discussed.
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