Il Nuovo Cimento A (1971-1996)

, Volume 43, Issue 2, pp 258–324 | Cite as

Practical theory of three-particle states

II. — Relativistic, spin zero
  • D. Z. Freedman
  • C. Lovelace
  • J. M. Namyslowski


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 Omnès, 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).


Si ottengono equazioni covarianti per lo scattering di particelle composte. Esse sono equazioni integrali lineari accoppiate in una variabile. Le soluzioni soddisfano l’unitarietà di tre particelle e tutti gli osservabili nei sistemi di tre particelle possono essere espressi in funzione di esse. Le equazioni sono dedotte dalla teoria dei campi, con l’approssimazione fondamentale che ogni sottosistema di due particelle sia dominato dai suoi stati legati a risonanze. Tuttavia le equazioni finali implicano solo le funzioni d’onda delle particelle composte e non il lagrangiano originario. Si tiene correttamente conto delle risonanze sovrapposte e si includono anche alcune forze di tre corpi. Il « potenziale » è essenzialmente il meccanismo di Peierls e la sua parte immaginaria dà l’effetto di interferenza fra le risonanze sovrapposte. Le nostre equazioni sono diverse e più semplici di quelle diAlessandrini eOmnès, perchè si sono eliminate le energie relative in maniera compatibile con le regole di Landau-Cutkosky. Nel presente lavoro si danno le equazioni solo per il caso in cui le particelle elementari sono prive di spin (masse disuguali).


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Copyright information

© Società Italiana di Fisica 1966

Authors and Affiliations

  • D. Z. Freedman
    • 1
    • 2
  • C. Lovelace
    • 1
    • 2
  • J. M. Namyslowski
    • 1
    • 2
  1. 1.Imperial CollegeLondon
  2. 2.CERNGeneva

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