On the compositeness criteria in field theories. - III

Abstract

The equivalence of a composite particle with an elementary one with vanishing wave-function renormalization is proved in the three-particle sector of the Lee model. The composite model chosen is one in which, in addition to usual Lee-model Hamiltonian, a separable interaction is also present in the V-θ sector. This model, in the limit of vanishing wave function renormalization constant for the U particle, is shown to lead to results for the V-θ scattering amplitude and the renormalized UVθ coupling constant, which are identical to those obtained by Bronzan using an elementary U particle in the V-θ sector. No restriction is imposed thereby on the vertex renormalization constant.