A field-theoretical model of pion-deuteron processes. II. Extended Fadde'ev and Amado-Lovelace equations

Abstract

For pt.I see ibid., vol.4, no.9, p.1371 (1978). A complete solution is presented to the novel disconnectedness problem encountered in a recent study of a simple field-theory model of the NN pi system. The five disconnectedness classes of the problem, coupled through a non-Abelian 'disconnectedness-multiplication' law, are summed by a system of coupled equations, which in the framework of the model also provides a complete account of the connection between the renormalisation and disconnectedness problems. A 5*5 system of generalised Fadde'ev equations is derived which acquires a connected kernel after one iteration. On the basis of these equations, modified, effective transition operators between two-cluster channels are constructed and shown to obey integral equations of a generalised Alt-Grassberger-Sandhas type.