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Scattering in field theory

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Il Nuovo Cimento (1955-1965)

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 rμ 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 rμ 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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Authors and Affiliations

  1. Argonne National Laboratory, Lemont, Illinois

    H. Ekstein

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  1. H. Ekstein
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Work performed under the auspices of the U.S. Atomic Energy Commission.

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Ekstein, H. Scattering in field theory. Nuovo Cim 4, 1017–1058 (1956). https://doi.org/10.1007/BF02745471

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