LEVEL STRUCTURE OF DUAL-RESONANCE MODELS

In this paper the level structure of narrow-resonance models with duality is considered. We shall use to this purpose the multiparticle dual amplitudes recently proposed by several authors and shall study the structure of the residue of each pole in what concerns its factorizability. We find that for each energy eigenvalue E n =√s n the residue does indeed factorize in a finite number of terms (number of degenerate levels) and that this number increases with n like exp [cE n]. The physical interpretation of this wild increase is found in the essential many body nature of models consistent with duality. The appearence of states with imaginary coupling follows easily from the covariant, four-dimentional approach that we have taken and that insures absence of kinematical singularities. It is nevertheless found that a cancellation mechanism analogous to the one existing in Q.E.D. (Ward identities) occurs here too. Although the problem of a systematic cancellation of all ghosts in a realistic case has not been solved, we see that the leading and most troublesome ghosts are indeed eliminated in this way. © 1969 Società Italiana di Fisica.