Momentum-space analysis of relativistic two-body equations with confining interactions: Stability considerations

Quark-antiquark bound states are considered using a relativistic equal-time (ET) equation for two spin-1/2 particles that includes negative-energy com ponents of wave functions. In the limit where either particle's mass tends to infinity, the ET equation reduces to the one-body Dirac equation. The us e of a scalar confining interaction in the ET equation is found to produce imaginary eigenvalues for the bound-state energy, similar to the findings b ased on the Salpeter equation. Retardation effects predict a modified stati c interaction in which couplings to doubly negative components of the wave function vanish. This: modified static interaction eliminates the imaginary eigenvalues. However, the modified analysis can produce abnormal solutions with a large relative momentum between the quark and antiquark when used w ith a scalar confining interaction. Anomalous negative-energy components of wave functions result when a timelike vector confining interaction is used for equal mass quarks. In the one-body limit, the Klein instability occurs with timelike vector confinement. For stability without regard to the type of confinement, the negative-energy components of wave functions should be omitted. [S0556-2813(99)06003-3].