Simple relativistic quark models

A class of relativistic quark models motivated by QCD are investigated. This model has dual representations as models of mesons and nucleons or quarks and gluons. The model assumption is that the Hamiltonian can be divided into two parts; one that involves degrees of freedom in the same connected local and global color singlet and the remaining interactions that allow the connected local and global color singlets to interact. The first class of interactions results in infinite towers of bare particles with hadronic quantum numbers. All but a finite number of these remain stable when the second class of interactions are included. The model interactions are expressed in terms of sub-hadronic degrees of freedom, which determine the bare hadronic spectrum and the interactions involving the bare hadrons in terms of a small number of sub-hadronic model parameters. As a first test, this paper considers the simplest case of mesons that interact via a string-breaking interaction. One virtue of this model is that all of the bare meson masses and eigenfunctions can be computed analytically. In addition, the string breaking interaction leads to production vertices that can also be computed analytically. The relativistic wave functions have a light-front kinematic symmetry. The goal is to find a simple model based on sub-hadronic degrees of freedom that can provide an efficient qualitative consistent description of hadronic masses, lifetimes, cross sections, sea quark effects, and electromagnetic properties.