A Lower Bound to the Ground State Energy of a Boson System with Fermion Source

Abstract

With the density matrix method ground state energies are determined variationally using elements of the density matrix as variational parameters. The variation is constrained by representability conditions but our knowledge of these is incomplete. As a consequence, lower bounds to ground state energies are obtained. This method has been successfully applied to fermion systems and we review some earlier work on light nuclei and the berylium atom. Our main purpose here is to develop this method for applicaton to systems of bosons around a source. We give details for the case of vector bosons with spinor fermion source. Our lower bounds are remarkably close to upper bounds obtained using wave functions and hence form strong evidence supporting our view that the present method forms a powerful computational tool in many-body theory.