Radially symmetric solutions of Bethe-Salpeter equation

Abstract

New exact solutions are obtained of the Bethe-Salpeter equation for a pair of fermions, in the ladder approximation and for zero boson mass. The solutions are applicable for small but non-vanishing total energy, and for scalar or pseudoscalar boson fields with ordinary or derivate coupling. A boundary condition, similar to that applied to the Schrodinger equation in three dimensions, is proposed, which reduces the continuum of eigenvalues for the coupling constant to a set of discrete values, except in the case of s(s) coupling. It is pointed out that this boundary condition also implies the existence of a new quantum number, with properties similar to those of the "strangeness" number already used to classify the new particles.