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

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. [ABSTRACT FROM AUTHOR]

Copyright of International Journal of Theoretical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)