Skip to main content
SpringerLink
Log in

The Rigorous Analyticity-Unitarity Program and Its Success

  • Conference paper
  • First Online:
Quantum Field Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 558))

Abstract

We show how the combination of analyticity properties derived from local field theory and the unitarity condition (in particular positivity) leads to non-trivial physical results, including the proof of the “Froissart bound” from first principles and the existence of absolute bounds on the pion-pion scattering amplitude.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. M. Gell-Mann, M.L. Goldberger and W. Thirring, Phys.Rev. 95 (1954) 1612.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. H. Lehmann, K. Symanzik and W. Zimmermann, Nuovo Cimento (Serie 10) 1 (1955) 205.

    Article  MATH  MathSciNet  Google Scholar 

  3. M.L. Goldberger, Phys.Rev. 99 (1975) 979.

    Article  ADS  Google Scholar 

  4. N.N. Bogoliubov, B.V. Medvedev and M.K. Polivanov, Voprossy Teorii Dispersion-nyk Sootnoshenii, V. Shirkov et al. Eds., Moscow 1958; K. Symanzik, Phys.Rev. 105 (1957) 743; H. Lehmann, Suppl. Nuovo Cimento 14 (1959) 153.

    Google Scholar 

  5. W. Zimmermann, Nuovo Cimento 10 (1958) 597.

    Article  MATH  Google Scholar 

  6. V. Gribov, private communication (1997).

    Google Scholar 

  7. K. Hepp, private communication, Zurich, 1996.

    Google Scholar 

  8. M.L. Goldberger, in Proc. Intl. Conf. on High Energy Physics, CERN, Geneva, 1958, B. Ferretti ed., CERN Scientific Information Service, 1958, p. 208.

    Google Scholar 

  9. J. Bros, H. Epstein and V. Glaser, Commun.Math.Phys. 1 (1965) 240.

    Article  ADS  MathSciNet  Google Scholar 

  10. M. Gell-Mann, in Proc. 6th Annual Rochester Conf., J. Ballam, V.L Fitch, T. Fulton, K. Huang, R.R. Rau and S.B. Treiman eds., Interscience Publishers, New York 1956, p. 30.

    Google Scholar 

  11. H. Lehmann, Nuovo Cimento 10 (1958) 579.

    Article  MATH  Google Scholar 

  12. S. Mandelstam, Phys.Rev. 112 (1958) 1344.

    Article  ADS  MathSciNet  Google Scholar 

  13. M. Froissart, Phys.Rev. 123 (1961) 1053.

    Article  ADS  Google Scholar 

  14. A. Martin, Phys.Rev. 129 (1963) 1432; and in Proc. 1962 Conf. on High energy Physics at CERN, J. Prentki ed., CERN Scientific Information Service, 1962, p. 567.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. A. Martin, Nuovo Cimento 42 (1966) 901.

    Article  ADS  Google Scholar 

  16. G. Sommer, Nuovo Cimento A48 (1967) 92. In the special case of pion-nucleon scattering a special argument gives R = 4m2inπ. See D. Bessis and V. Glaser, Nuovo Cimento (Serie X) 50 (1967) 568.

    ADS  Google Scholar 

  17. Y.S. Jin and A. Martin, Phys.Rev. B135 (1964) 1375.

    Google Scholar 

  18. L. Lukaszuk and A. Martin, Nuovo Cimento 52 (1967) 122.

    Article  ADS  Google Scholar 

  19. J. Kupsch, Nuovo Cimento B70 (1982) 85.

    Google Scholar 

  20. H. Cheng and T.T. Wu, Phys.Rev.Lett. 24 (1970) 1456.

    Article  ADS  Google Scholar 

  21. N.N. Khuri and T. Kinoshita, Phys.Rev. B137 (1965) 720.

    Article  ADS  MathSciNet  Google Scholar 

  22. U. Amaldi et al., Phys.Lett. B44 (1973) 112; S.R. Amendoliaet al., Phys.Lett. B44 (1973) 119.

    ADS  Google Scholar 

  23. V. Bartenev et al., Phys.Rev.Lett. 31 (1973) 1367; U. Amaldi et al., Phys.Lett. 66B (1977) 390.

    Article  ADS  Google Scholar 

  24. G. Matthiae, Rep.Progr.Phys. 57 (1994) 743.

    Article  ADS  Google Scholar 

  25. N.N. Khuri, Rencontres de Physique de la vallée d’Aoste, 1994, M. Greco ed., Editions Frontieres 1994, p. 771; see also: N.N. Khuri and T.T. Wu, Phys.Rev. D56 (1997) 6779 and 6785.

    Google Scholar 

  26. Angela Faus-Golfe, private communication.

    Google Scholar 

  27. Y.Ya. Pomeranchuk, Soviet Phys. JETP 7 (1958) 499.

    Google Scholar 

  28. R.J. Eden, Phys.Rev.Lett. 16 (1966) 39.

    Article  ADS  MathSciNet  Google Scholar 

  29. T. Kinoshita, in Perspectives in Modern Physics, R.E. Marshak ed., New York 1966), p. 211; see also G. Grunberg and T.N. Truong, Phys.Rev.Lett. B31 (1973) 63.

    Google Scholar 

  30. A. Martin, Nuovo Cimento 44 (1966) 1219.

    Article  ADS  Google Scholar 

  31. A. Martin, Proceedings of the 1967 International Conference on Particles and Fields, C.I Hagen, G. Guralnik and V.A. Mathur, eds., John Wiley and Sons, New York 1967, p. 255.

    Google Scholar 

  32. A. Martin, Preprint, Institute of Theoretical Physics, Stanford University ITP-134 (1964), unpublished; A. Martin in “High Energy Physics and Elementary particles”, ICTP Trieste 1965, International Atomic Energy Agency Vienna (1965), p. 155; L. Lukaszuk and A. Martin, Nuovo Cimento A47 (1967) 265; J.B. Healy, Phys.Rev. D8 (1973) 1907; G. Auberson, L. Epele, G. Mahoux and R.F.A. Simao, Nud.Phys. B94 (1975) 311; C. Lopez and G. Mennessier, Phys.Lett. B58 (1975) 437; B. Bonnier, C. Lopez and G. Mennessier, Phys.Lett. B60 (1975) 63; C. Lopez and G. Mennessier, Nud.Phys. B118 (1977) 426.

    Google Scholar 

  33. I. Caprini and P. Dita, Preprint, Institute of Physics and Engineering, P.O. Box 5206, Bucharest (1978), unpublished. The initial work on this lower bound was: B. Bonnier and R. Vinh Mau, Phys.Rev. 165 (1968) 1923.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theoretical Physics Division, CERN, CH-1211, Geneva 23, Switzerland

    André Martin

  2. LAPP, F-74941, Annecy le Vieux, France

    André Martin

Authors
  1. André Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, Föhringer Ring 6, 80805, München, Germany

    Peter Breitenlohner  & Dieter Maison  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Martin, A. (2000). The Rigorous Analyticity-Unitarity Program and Its Success. In: Breitenlohner, P., Maison, D. (eds) Quantum Field Theory. Lecture Notes in Physics, vol 558. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44482-3_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-44482-3_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67972-1

  • Online ISBN: 978-3-540-44482-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation