Integrable quantum field theories with unstable particles

A new family of S-matrix theories with resonance poles is constructed and c onjectured to correspond to the Homogeneous sine-Gordon theories associated with simply laced compact Lie groups, where some of the resonance pales ca n be traced to the presence of unstable particles in the spectrum. These th eories are unitary in the usual SStau = 1 sense, they are not parity invari ant, and they exhibit continuous coupling constants that determine both the mass spectrum of stable particles and the masses and the position of the r esonance poles. (C) 2000 Published by Elsevier Science B.V. All rights rese rved.