General Theory of Multiple Poles and Coinciding Simple Poles

Abstract

It is investigated in the general framework of the Bethe-Salpeter formalism how multiple poles of the scattering Green's function are synthesized out of coinciding simple poles. A necessary and sufficient condition for the existence of the leading multiple pole is obtained and applied to some concrete examples. The residues of multiple poles and the corresponding generalized Bethe-Salpeter amplitudes are expressed in terms of the residues of simple poles and the ordinary Bethe-Salpeter amplitudes, respectively. Some comments are made on the conspiracy problem from the standpoint of the multiple-pole theory.