Quark models of hadron interactions

Quark models of single hadrons have been successful in accounting for hadron spectroscopy. They are not automatically applicable to multi-hadron dynamics. The authors are investigating quark models of multi-hadron dynamics which emphasize the following features: (1) spatial confinement of quarks is tied to color confinement (gauge invariance), (2) absence of long-range Van der Waals forces, (3) Poincare invariance. Starting from ideas due to Greenberg and Hietarinta the authors realize these requirements in zeroth order by models which feature quarks confined to noninteracting hadrons, each of which has infinitely many stable excited states. The authors have investigated in detail the mathematical properties of models consisting of quark-antiquark systems coupled to two-quark-two-antiquark states, and developed a particular implementation suitable for numerical studies. Preliminary results are encouraging