Relativistic \(n\)-body wave equations in scalar quantum field theory. (English) Zbl 1248.81104
Summary: The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic \(n\)-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic \(n\)-body wave equations. The equations are shown to have the Schrödinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the \(n\)-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields.
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