ON THE LORENTZ STRUCTURE OF THE CONFINING POTENTIAL IN THE INSTANTANEOUS BETHE-SALPETER-EQUATION

We investigate the Lorentz structure of the confining potential throug h a study of the meson spectrum using Salpeter's instantaneous approxi mation to the Bethe-Salpeter equation. The equivalence between Salpete r's and a random-phase-approximation (RPA) equation enables one to emp loy the same techniques developed by Thouless, in his study of nuclear collective excitations, to test the stability of the solutions. The s tability analysis reveals the existence of imaginary eigenvalues for a confining potential that transforms as a Lorentz scalar. Moreover, we argue that the instability persists even for very large values of the constituent quark mass. In contrast, we find no evidence of imaginary eigenvalues for a timelike vector potential - even for very small val ues of the constituent mass.