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Il Nuovo Cimento A (1965-1970)

, Volume 44, Issue 4, pp 1081–1090 | Cite as

The cross-discontinuity condition inS-matrix theory

  • D. Branson
Article

Summary

In recent work onS-matrix discontinuity equations it has been conjectured that the terms in a unitarity equation associated with a normal threshold discontinuity in one channel have no normal threshold singularities in overlapping crossed channels. AnS-matrix theory proof of this conjecture is given for simple cases, but it is shown that when intermediate states of four or more particles are involved, the conjecture is true only if the particles in the intermediate state are sufficiently near threshold. The impact of this result on previous work is discussed.

Keywords

Branch Point Integration Region Singularity Curve Normal Threshold Prova 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Riassunto

Nei recenti articoli sulle equazioni di discontinuità della matriceS si è fatta la congettura che i termini di un'equazione di unitarietà associata ad una discontinuità di soglia normale in un canale non hanno singolarità di soglia normale in canali incrociati che si sovrappongono. Si dà una prova di questa congettura nella teoria della matrice,S per casi semplici, ma si mostra che quando sono coinvolti stati intermedi di quattro o più particelle, la congettura è vera solo se le particelle nello stato intermedio sono sufficientemente vicine alla soglia. Si discute la rilevanza di questo risultato sugli articoli precedenti.

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References

  1. (1).
    D. I. Olive:Nuovo Cimento,37, 1422 (1965).MathSciNetCrossRefGoogle Scholar
  2. (2).
    H. P. Stapp:Lectures on the Analytic Structure of Many-Particle Scattering Amplitudes, International Centre for Theoretical Physics, Trieste, 1965.Google Scholar
  3. (3).
    For an explanation of the bubble notation seeD. I., Olive:Phys. Rev.,135, B 745 (1964).ADSMathSciNetCrossRefGoogle Scholar
  4. (4).
    O. Steinmann:Helv. Phys. Acta,33, 257, 347 (1960).MathSciNetGoogle Scholar
  5. (5).
    R. E. Cutkosky:Journ. Math. Phys.,1, 429 (1960).ADSMathSciNetCrossRefGoogle Scholar
  6. (6).
    P. V. Landshoff andD. I. Olive:Extraction of Singularities from the S-Matrix, University of Cambridge preprint.Google Scholar
  7. (7).
    P. V. Landshoff, D. I. Olive andJ. C. Polkinghorne:The Hierarchical Principle in Perturbation Theory, University of Cambridge preprint.Google Scholar

Copyright information

© Società Italiana di Fisica 1966

Authors and Affiliations

  • D. Branson
    • 1
  1. 1.Lawrence Radiation LaboratoryUniversity of CaliforniaBerkeley

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