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Il Nuovo Cimento (1955-1965)

, Volume 18, Issue 5, pp 947–956 | Cite as

Bound states, shadow states and mandelstam representation

  • T. Regge
Article

Summary

In a previous paper a technique involving complex angular momenta was used in order to prove the Mandelstam representation for potential scattering. One of the results was that the number of subtractions in the transmitted momentum depends critically on the location of the poles (shadow states) of the scattering matrix as a function of the complex orbital momentum. In this paper the study of the position of the shadow states is carried out in much greater detail. We give also related inequalities concerning bound states and resonances. The physical interpretation of the shadow states is then discussed.

Riassunto

In questo lavoro si estendono i risultati di una nota precedente dell’autore in cui si è fatto uso di momenti angolari complessi. In particolare vengono derivate ineguaglianze concernenti il numero di sottrazioni nelle regole di dispersione alla Mandelstam per vari tipi di potenziale tra cui il potenziale di Yukawa.

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References

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    T. Regge:Nuovo Cimento,14, 951 (1959).MathSciNetCrossRefMATHGoogle Scholar
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    R. Blankenbecler, M. L. Coldberger, M. N. Khuri andS. B. Treiman:Ann. of Phys.,10, 62 (1960).ADSCrossRefGoogle Scholar
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    A. Klein:Journ. Math. Phys.,1, 41 (1960).ADSCrossRefMATHGoogle Scholar
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    L. Fonda, L. A. Radicati andT. Regge:Mandelstam representation for the non-relativistic many channel problem (in proof).Google Scholar
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    E. T. Whittaker andG. N. Watson:A Course of Modern Analysis (Cambridge, 1952).Google Scholar
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    B. Levy andJ. Keller:Diffraction on a smooth object.Google Scholar

Copyright information

© Società Italiana di Fisica 1960

Authors and Affiliations

  • T. Regge
    • 1
    • 2
  1. 1.Palmer Physical LaboratoryPrinceton UniversityPrinceton
  2. 2.Department of PhysicsUniversity of RochesterRochester

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