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Il Nuovo Cimento A (1965-1970)

, Volume 45, Issue 2, pp 207–224 | Cite as

Study of the roy equations

II. — Proof of the existence of a solution
  • T. P. Pool
Article

Summary

The Roy equations express the real parts of the partialwave ππ amplitudes in terms of two scattering lengths and of singular integrals of the imaginary parts of these amplitudes. Combining these equations with unitarity, one obtains an infinite coupled system of nonlinear singular integral equations for the imaginary parts. Using the fixed-point theorem of Banach-Cacciopoli, one can prove that this system has a solution for a restricted range of the energy variable.

Исследование уравнений Роя. — II. Докаэательство сушествования рещения

Реэюме

Уравнения Роя выражают вешественные части парциальных ππамплитуд череэ две длины рассеяния и череэ сингулярные интегралы мнимых частей зтих амплитуд. Общединяя зти уравнения с унитарностью, получается бесконечная свяэанная система нелинейных сингулярных интегральных уравнений для мнимых частей. Испольэуя теорему Банаха-Каччополи, можно докаэать, что зта система имеет рещение для ограниченной области по переменной знергии.

Riassunto

Le equazioni di Roy esprimono le parti reali delle ampiezze ππ d’onda parziale sulla base di due lunghezze di scattering e di integrali singolari delle parti immaginarie di queste ampiezze. Combinando queste equazioni con l’unitarietà, si ottiene un sistema accoppiato infinito di equazioni non lineari, singolari e integrali per le parti immaginarie. Usando il teorema del punto fisso di Banach-Cacciopoli, si può provare che questo sistema ha una soluzione per un intervallo di valori ristretto della variabile di energia.

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References

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Copyright information

© Società Italiana di Fisica 1978

Authors and Affiliations

  • T. P. Pool
    • 1
  1. 1.Fachbereich PhysikUniversität KaiserslauternKaiserslauternBRD

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