Comparing relativistic three-body wave equations with non-relativistic bound-states results in scalar QFT

Abstract

We use the variational method in a reformulated model of quantum field theory to compare the three-body relativistic wave equations with non-relativistic equations for our scalar system (consisting of one particle and two antipaticles) interacting via a massless or massive mediating scalar field. Simple Fock-space variational trial states have been employed to derive the equations. Ground state solutions of the relativistic and non-relativistic three-body systems for bound-states equations are obtained and compared for different strengths of coupling, for both massive and massless mediating fields. The relativistic three-body energy solutions are above the non-relativistic results in the present model. In the current formalism we have no negative energy solutions.