Practical theory of three-particle states

We obtain covariant equations for the scattering of composite particles. They are coupled linear integral equations in one variable. The solutions satisfy three-particle unitarity, and all observables in three-particle systems can be expressed in terms of them. The equations are derived from field theory, the basic approximation being that each two-particle subsystem is dominated by its bound states and resonances. However, the final equations involve only the wave functions of the composite particles, and not the original Lagrangian. Overlapping resonances are correctly taken into account, and some three-body forces are also included. The « potential » is essentially the Peierls mechanism, and its imaginary part gives the interference effect between overlapping resonances. Our equations are different from and simpler than those of Alessandrini and Omnes, because we eliminate the relative energies in a way compatible with the Landau-Cutkosky rules. The present paper only gives the equations when the elementary particles are spinless (unequal masses).