Relativistic oscillator in a Bethe-Salpeter model: nonexistence of discrete bound states

We investigate the solutions of the covariant Bethe-Salpeter equation for bound states of a scalar quark-antiquark system with an effective confining kernel which in coordinate four-space behaves as R2. Using a suitable set of new variables we separate the equation into one-dimensional equations and study the eigenvalue problem. We find that the covariant bound-state Bethe-Salpeter equation with the above kernel possesses only a continuous spectrum