Equivalence problems in models with infinite renormalization and unstable particles

Abstract

The equivalence problems in two models with unstable particles and infinite mass and charge renormalizations are investigated with respect to observable effects and to the details of Hilbert-space formalism. The concept of resonance both as a product of decay of a bare quantum and as a pure dynamical phenomenon is introduced. The equivalence conditions between the models are thus equivalence conditions for one or another description. The models are of Lee-model type with relativistic kinematics. The analysis of the resonance is made in the «point-coupling» limit (cut-off functions completely removed).