Relativistic wave equations of combined three particles and three antiparticles in scalar quantum field theory

Abstract

The recent observation of a positronium molecule (e−e+e−e+) by Cassidy and Mills (D B Cassidy and A P Mills 2007 Nature (London) 449 195) raises interest in other (fermionic) exotic systems. Similarly, the question arises whether larger bosonic systems can be formed. The variational method in a reformulated Hamiltonian formalism of quantum field theory is used to derive relativistic wave equations for a system consisting of three scalar particles and three scalar antiparticles (six-body problem) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic six-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. Approximate ground-state solutions of the six-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields.