Can the S-matrix be generated from its lowest-order term?

Abstract

The suggestion that the S-matrix can be generated from its lowest-order term by successive applications of the unitarity and causality conditions, is tested on a simple example. It is shown that the procedure is vitiated by the breakdown of the expansion near resonance, which makes an application of the Kramers-Kronig relations to the separate terms impossible. In the case of propagation of waves through a medium the state of affairs is analogous.