Algebraic meson models

We discuss two meson models where a meson is described in the Bethe-Salpeter formalism as a bound state of a quark and an antiquark interacting via an instantaneous infinite square-well potential. In the first model the quark and antiquark are heavy and the depth of the potential exactly balances their rest energy and in the second model the quark and antiquark are massless. In each model the mass operator for the composite system is homogeneous. Hence a dilatation operator can be defined such that the mass operator transforms in the same way as the translation generator under infinitesimal scale transformations. Then the quark-antiquark bound states carry irreducible representations of the Weyl Lie algebra which, due to the scale parameter introduced by the finite width of the infinite square-well potential, have nontrivial discrete mass spectra.