Skip to main content
SpringerLink
Log in

Polynomial behaviour of scattering amplitudes at fixed momentum transfer in theories with local observables

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

It is shown that, in theories of exactly localized observables, of the type proposed byAraki andHaag, the reaction amplitude for two particles giving two particles is polynomially bounded ins for fixed momentum transfert<0. The proof does not need observables localized in space-time regions of arbitrarily small volume, but uses relativistic invariance in an essential way. It is given for the case of spinless neutral particles, but is easily extendable to all cases of charge and spin. The proof can also be generalized to the case of particles described by regularized products

$$\int {\varphi (x_1 ,..., x_n ) \phi _1 } (x - x_1 ) ... \phi _n (x - x_n )dx_1 ...dx_n $$

ofWightman orJaffe fields.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Araki, H.: Einführung in die Axiomatische Quantenfeldtheorie, E. T. H. (1961–1962).

  2. -- Varenna Lectures (1968), to be published.

  3. Haag, R., andB. Schroer: J. Math. Phys.3, 248 (1962).

    Google Scholar 

  4. Borchers, H. J.: In: Applications of mathematics to problems in theoretical physics, edited by F. Lurçat. New York: Gordon and Breach 1967.

    Google Scholar 

  5. Epstein, H.: J. Math. Phys.8, 750 (1967).

    Google Scholar 

  6. Bros, J., H. Epstein, andV. Glaser: Commun. Math. Phys.1, 240 (1965).

    Google Scholar 

  7. Epstein, H.: In: Axiomatic field theory. Chrétien and Deser, eds., New York: Gordon and Breach 1966.

    Google Scholar 

  8. Bros, J., H. Epstein, andV. Glaser: Nuovo Cimento31, 1265 (1964).

    Google Scholar 

  9. —— —— —— Commun. Math. Phys.6, 77 (1967).

    Google Scholar 

  10. Weyl, H.: Classical groups. Princeton, N. J.: Princeton University Press 1946.

    Google Scholar 

  11. Bogoliubov, N. N., B. V. Medvedev, andM. K. Polivanov: Voprossy teorii dispersionnykh sootnoshenii. Moscow 1958.

  12. Bremermann, H., R. Oehme, andJ. G. Taylor: Phys. Rev.109, 2178 (1958).

    Google Scholar 

  13. Lehmann, H.: Nuovo Cimento Suppl.14, 153 (1959).

    Google Scholar 

  14. Froissart, M.: In: Dispersion relations and their connection with causality. New York: Academic Press 1964.

    Google Scholar 

  15. Hepp, K.: Helv. Phys. Acta37, 639 (1964).

    Google Scholar 

  16. Martin, A.: Brandeis Lectures (1967), to be published. These lectures contain references to the original articles.

  17. Streater, R. F.: J. Math. Phys.3, 256 (1962).

    Google Scholar 

  18. Jost, R.: The general theory of quantized fields, A. Math. Soc., Providence, Rhode Island (1965), p. 81.

    Google Scholar 

  19. Boas, R. P.: Entire functions. p. 22. New York: Academic Press 1954.

    Google Scholar 

  20. Ref. [15], p. 48

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CERN, Geneva

    H. Epstein, V. Glaser & A. Martin

Authors
  1. H. Epstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Glaser
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Epstein, H., Glaser, V. & Martin, A. Polynomial behaviour of scattering amplitudes at fixed momentum transfer in theories with local observables. Commun.Math. Phys. 13, 257–316 (1969). https://doi.org/10.1007/BF01645415

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01645415

Keywords

Search

Navigation