Relativistic wave equations of n-body systems of particles and antiparticles of various masses in scalar quantum field theory

Abstract

A generalization of the scalar Yukawa model to include many ‘flavors’ of scalar particles and antiparticles is considered. The variational method within the Hamiltonian formalism of quantum field theory is used to derive relativistic n-body wave equations for stationary systems consisting of scalar particles and antiparticles where all the particles and antiparticles have different masses. Using a simple ansatz we derive the relativistic n-body wave equations for any n integer number. 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. 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.