Stability of the spectator, Dirac, and Salpeter equations for mesons

Masons are made of quark-antiquark pairs held together by the strong force. The one channel spectator, Dirac, and Salpeter equations can each be used to model this pairing. We look at cases where the relativistic kernel of th ese equations corresponds to a timelike vector exchange, a scalar exchange, or a linear combination of the two. Since the model used in this paper des cribes mesons which cannot decay physically, the equations must describe st able states. We find that this requirement is not always satisfied, and giv e a complete discussion of the conditions under which the various equations give unphysical, unstable solutions. [S0556-2813(99)05902-6].