On Vertical Representation of Bethe-Salpeter Amplitudes

The Bethe-Salpeter equation for S-wave bound states of two scalar particles with equal mass interacting via scalar mesons is considered in the ladder approximation. It is shown that an integral representation previously attempted holds for all the solutions, normal and abnormal, of the B-S equation. Use is made of the fact that the B-S equation under consideration can be written in a form of an integral equation with a real symmetric and positive kernel. Also given is a limitation on the lowest eigenvalue of such an integral kernel in terms of its first and second traces.