Model for the Two-Pion and Three-Pion Resonances

A relativistic model of $\pi -\pi$ interaction is proposed from analogy with field theory. The main assumption in the model is that the interaction kernel is separable in momentum space. A Frazer-Fulco type resonance formula for the isovector $2\pi$ resonance is exactly derived on this model and its parameters are determined from the observed $2\pi$ resonance at 750 MeV.