Use of a non-relativistic basis for describing the low energy meson spectrum

Abstract

We justify the use of harmonic oscillator eigenfunctions for expanding the fermionic fields of an effective field theory and evaluate its utility for solving a Hamiltonian inspired by the QCD formalism in the Coulomb Gauge. Since the functions involved in such expansion are non-relativistic, the Talmi-Moshinsky transformations can be used to recover the translational invariance of the center of mass of the mesonic states. Finally, many-body methods and an <i>a posteriori</i> flavor mixing procedure are used to compute a preliminary spectrum for the mesons below 1 GeV.