Introduction to the Use of Non-Linear Techniques in S-Matrix Theory

  • D. Atkinson
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 7/1970)


I am going to explain to you how one can tackle certain problems in S-matrix theory that involve nonlinear functional equations. A physicist’s usual reaction to a non-linear equation of this kind would be either to try to get an approximate solution by iteration, or to introduce a linearization, perhaps in the neighbourhood of a known approximate solution. I will introduce some concepts of Banach space analysis [1], which will enable us to put these intuitive ideas on a rigorous basis. The advantage is that one can sometimes prove the existence of solutions of the exact equations, without any approximations.


Banach Space Cauchy Sequence Contraction Mapping Contraction Mapping Principle Elastic Unitarity 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. A. Krasnoselskii,Topological Methods in the Theory of Nonlinear Integral Equations- McMillan, London and New York (1964).Google Scholar
  2. 2.
    A. Martin, Nuovo Cimento 59A, 131 (1969).ADSGoogle Scholar
  3. 3.
    V. V. Serebryakov and D. V. Shirkov, Fortschr. d. Phys. 13, 227 (1965).MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    R. L. Warnock, Phys. Rev. 170, 1323 (1968).ADSCrossRefGoogle Scholar
  5. 5.
    S. Mandelstam, Phys. Rev. ll2, 1344 (1958); 115, 1741, 1752 (1959).MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    D. Atkinson, Nucl. Phys. B7, 375 (1968); B8, 377 (1968).ADSCrossRefGoogle Scholar
  7. 7.
    D. Atkinson, Nucl. Phys. B13, 415 (1969).ADSCrossRefGoogle Scholar
  8. 8.
    J. Kupsch, Nucl. Phys. B11, 573 (1969); B12, 155 (1969).MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    D. Atkinson and R. L. Warnock, to be published in Phys. Rev.Google Scholar
  10. 10.
    D. Atkinson, CERN preprint (in preparation).Google Scholar

Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • D. Atkinson
    • 1
  1. 1.CERNGenevaSwitzerland

Personalised recommendations