Covariance properties of a multifermion Hamiltonian with pairwise, massless vector-boson exchange

Abstract

We investigate the Poincare covariance of the Hamiltonian of aN-fermion system, in which the two-body interaction is produced by the exchange of a massless vector boson with a nonconstant form factor at vertices. The relativistic separation of center-of-mass and internal-motion variables is performed by exploiting an approach developed some years ago by Krajcik and Foldy. It is shown that, in order to ensure that theN-fermion Hamiltonian (expanded up to the order 1/c2) is the time-translation generator of the Poincare algebra, one requires a correct treatment of the form factor at the order considered, and, for noncommuting particle «charges», the inclusion in the potential of three-body terms, whose expression is explicitly derived. A preliminary analysis of the effect of such terms is given for baryons and deuterium in the framework of the constituent quark model.