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

• Published in: Journal of physics. G, Nuclear and particle physics Nuclear and particle physics, 2010-02, Vol.37 (2), p.025007-025007 (15)
• Main Authors: Emami-Razavi, Mohsen, Bergeron, Nantel, Darewych, Jurij W
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Nuclear physics; Physics; The physics of elementary particles and fields
• ISSN: 0954-3899; 1361-6471
• DOI: 10.1088/0954-3899/37/2/025007

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 Schrodinger 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.