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Approximate production amplitudes without complex singularities

  • John Cunningham
Article

Abstract

A decomposition of the five point single loop amplitude into a sum over four point amplitudes is used to suppress the contributions of some contracted diagrams at and near specified values of the fixed invariants in such a way as to admit the possibility of single variable dispersion relations without the use of complex integration contours.

Keywords

Dispersion Relation Internal Line Invariant Variable Principal Minor Complex Singularity 
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References

  1. 1.
    R. Karplus, C. M. Sommerefield andE. H. Wichmann, Phys. Rev.,111, 1187, 1958 and Phys. Rev.,114, 376, 1959.MATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    G. Källen andA. S. Wightman, Mat. Fys. Skr. Dan. Vid. Selsk.,1, No. 6, 1958.Google Scholar
  3. 3.
    S. Mandelstam, Phys. Rev.,112, 1344, 1958, Phys. Rev.,115, 1741, 1959 and Phys. Rev.,115, 1752, 1959.CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    R. Oehme, Phys. Rev.,111, 1430, 1958.MATHCrossRefADSMathSciNetGoogle Scholar
  5. 5.
    J. Tarski, J. Math. Phys.,1, 149, 1960.MATHCrossRefADSMathSciNetGoogle Scholar
  6. 6.
    T. Regge andG. Barucchi, Nuovo Cimento,34, 106, 1964.CrossRefMathSciNetGoogle Scholar
  7. 7.
    L. F. Cook andJ. Tarski, J. Math. Phys.,3, 1, 1962.MATHCrossRefADSMathSciNetGoogle Scholar
  8. 8.
    P. V. Landshoff andS. B. Trieman, Nuovo Cimento,19, 1249, 1961.CrossRefGoogle Scholar
  9. 9.
    R. F. Alvarez-Estrada, Nuovo Cimento,13A, 1, 1973.ADSMathSciNetGoogle Scholar
  10. 10.
    J. S. Frederiksen, Groningen preprint, 1972, to appear in J. Math. Phys.Google Scholar
  11. 11.
    J. Cunningham, Aust. J. Phys.,17, 553, 1964.ADSMathSciNetGoogle Scholar
  12. 12.
    J. C. Polkinghorne, Nuovo Cimento,4, 216, 1956.MATHMathSciNetGoogle Scholar
  13. 13.
    T. W. B. Kibble, Proc. Roy. Soc.,A224, 355, 1958.ADSGoogle Scholar
  14. 14.
    H. R. Screaton, Nuovo Cimento,11, 229, 1959.MATHCrossRefGoogle Scholar
  15. 15.
    A. A. Logunov andA. N. Taukhelidze, Nucl. Phys.,8, 374, 1958 and Nuovo Cimento,10, 943, 1958,A. A. Logunov andI. T. Todorov, Nucl. Phys.,10, 552, 1959.MATHCrossRefGoogle Scholar
  16. 16.
    Y. S. Kim, Phys. Rev. Letters,6, 313, 1961.CrossRefADSGoogle Scholar
  17. 17.
    J. Cunningham, Aust. J. Phys.,17, 161, 1964.ADSMathSciNetGoogle Scholar
  18. 18.
    R. J. Eden, P. V. Landshoff, D. I. Oilve andJ. C. Polkinghorne, The analytic S-matrix, Cambridge, 1966.Google Scholar
  19. 19.
    J. Cunningham, Rev. Mod. Phys.,36, 833, 1964 and Fortschritte der Physik,19, 613, 1971.CrossRefADSMathSciNetGoogle Scholar
  20. 20.
    I. T. Todorov, Analytic properties of Feynman diagrams in quantum field theory, Pergamon, 1971.Google Scholar
  21. 21.
    L D. Landau, Nucl. Phys.,13, 181, 1959.MATHCrossRefGoogle Scholar
  22. 22.
    L. M. Brown, Nuovo Cimento,22, 178, 1961.MATHCrossRefGoogle Scholar
  23. 23.
    D. B. Melrose, Nuovo Cimento,40, 181, 1965.MATHCrossRefADSMathSciNetGoogle Scholar
  24. 24.
    F. R. Halpern, Phys. Rev. Letters,10, 310, 1963.CrossRefADSGoogle Scholar
  25. 25.
    M. Giffon, Nuovo Cimento,61A, 663, 1969.ADSGoogle Scholar

Copyright information

© with the authors 1974

Authors and Affiliations

  • John Cunningham
    • 1
  1. 1.School of Mathematics and Computer ScienceUniversity College of North WalesBangorU. K.

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