Influence of the self-energy diagrams on the solutions of a scalar Bethe-Salpeter equation

The influence of self-energy diagrams on solutions of the Bethe-Salpeter equation is studied by taking a gphi*//sub 1/(x)phi/sub 1/(x)phi/sub 2/(x) interaction in the ladder approximation. The results show that for ground-state solutions the self-energy diagrams will diminish the eigenvalues and alter the wave functions slightly. However, for the excited states and antisymmetric solutions, the influence of the self-energy diagrams is considerable, and completely alters the properties of the solutions. Their wave functions look like a delta function and their eigenvalues are independent of the binding energy and the quantum numbers. The results also show that the infrared behavior of the self-energy diagrams is very important for the solutions of the equation, and that the solutions from the ladder approximation are meaningful only in the loosely bound cases. As the binding becomes tight, the contribution from the self-energy diagrams becomes important.