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Il Nuovo Cimento (1955-1965)

, Volume 4, Issue 5, pp 1017–1058 | Cite as

Scattering in field theory

  • H. Ekstein
Article

Summary

A precise statement of the scattering problem, general enough to include composite particles in field theory, is proposed: the four Heisenberg operatorsP μ which represent the total energy-momentum vector, can be expressed asymptotically (t → ± ∞) as integrals of mutually commuting operatorsA r (±)+ (k)k A r (±) (k) which represent the four-momenta of the incident and outgoing particles, both elementary and composite. For a theory given in terms of bare-particle creation operators a r , the problem consists in finding the asymptotic operators A(±) as functions of thea r anda r . A system of linear equations for this purpose is derived. Alternatively, theS-matrix can be obtained by solving a bi-linear equation, the inhomogeneous term of which consists essentially of products of one-particle state vectors.

Riassunto

Si propone una precisa enunciazione del problema dello scattering, abbastanza generale per comprendere nella teoria dei campi Je particelle composte: i quattro operatori di Heisenberg Pμ che rappresentano il vettore energia-momento totale possono essere espressi asintoticamente (t → ± ∞) corne integrali di operatori che mutuamente commutanoA r (±)+ (k)k A r (±) (k) che rappresentano i quadrimomenti delle particelle incidenti ed uscenti, sia elementari che composte. Per una teoria esposta in termini di operatori a r + di particelle nude, il problema consiste nel trovare gli operatori A(±) asintotici in funzione delle ar e a r + . A tale scopo si deriva un sistema di equazioni lineari. In alternativa si può ottenere la matrice S risolvendo un’equazione bilineare il cui termine inomogeneo è formato essenzialmente da prodotti di vettori di uno stato singolo.

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Copyright information

© Società Italiana di Fisica 1956

Authors and Affiliations

  • H. Ekstein
    • 1
  1. 1.Argonne National LaboratoryLemont

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