Skip to main content
SpringerLink
Log in

Positivity of Wightman functionals and the existence of local nets

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

Abstract

The paper is concerned with the existence of a local net of von Neumann algebras associated with a given Wightman field. For fields satisfying a generalizedH-bound the existence of such a net is shown to be equivalent to a certain positivity property of the Wightman distributions.

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. Alcántara-Bode, J., Yngvason, J.: Ann. Inst. Henri Poincaré48, 147 (1988)

    Google Scholar 

  2. Araki, H.: Einführung in die axiomatische Quantenfeldtheorie. ETH Zürich, 1962

  3. Araki, H.: Local quantum theory. In: Proceedings of the international school of physics. Enrico Fermi. Corse XLV, 1968. Jost, R. (ed.). Soc. It. di Fisica, Bologna, 1968

    Google Scholar 

  4. Bisogniano, J.J., Wichmann, E.H.: J. Math. Phys.16, 985 (1975)

    Google Scholar 

  5. Bisogniano, J.J., Wichmann, E.H.: J. Math. Phys.17, 303 (1976)

    Google Scholar 

  6. Borchers, H.J.: Nuovo Cim.15, 794 (1960)

    Google Scholar 

  7. Borchers, H.J.: Nuovo Cim.24, 214 (1962)

    Google Scholar 

  8. Borchers, H.J., Yngvason, J.: Commun. Math. Phys.42, 231 (1975)

    Google Scholar 

  9. Borchers, H.J., Yngvason, J.: Commun. Math. Phys.43, 255 (1975)

    Google Scholar 

  10. Borchers, H.J., Yngvason, J.: Partially commutative moment problems. Preprint, 1989

  11. Borchers, H.J., Zimmermann, W.: Nuovo Cim.31, 1047 (1964)

    Google Scholar 

  12. Buchholz, D.: On Quantum fields which generate local algebras. Preprint, 1988

  13. Driessler, W., Fröhlich, J.: Ann. Inst. Henri Poincaré27, 221 (1977)

    Google Scholar 

  14. Driessler, W., Summers, S.J., Wichmann, E.H.: Commun. Math. Phys.105, 49 (1986)

    Google Scholar 

  15. Dubois-Violette, M.: Commun. Math. Phys.43, 225 (1975); Commun. Math. Phys.54, 151 (1977)

    Google Scholar 

  16. Fredenhagen, K., Hertel, J.: Commun. Math. Phys.80, 555 (1981)

    Google Scholar 

  17. Gachok, V.P.: Nuovo Cim.45A, 784 (1966)

    Google Scholar 

  18. Glimm, J., Jaffe, A.: Quantum Physics. Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

  19. Haag, R., Kastler, D.: J. Math. Phys.5, 848 (1964)

    Google Scholar 

  20. Jost, R.: The general theory of quantized fields. Providence RI: Am. Math. Soc. 1963

    Google Scholar 

  21. Powers, R.T.: Commun. Math. Phys.21, 85 (1971)

    Google Scholar 

  22. Powers, R.T.: Trans. Am. Math. Soc.187, 261 (1974)

    Google Scholar 

  23. Rehberg, J., Wollenberg, M.: Math. Nachr.125, 1 (1986)

    Google Scholar 

  24. Peressini, A.L.: Ordered topological, vector spaces. New York: Harper & Row 1967

    Google Scholar 

  25. Streater, R.F., Wightman, A.S.: PCT spin and statistics and all that. Reading, MA: Benjamin 1964

    Google Scholar 

  26. Summers, S.J.: Helv. Phys. Acta60, 1004 (1987)

    Google Scholar 

  27. Wollenberg, M.: Rep. Math. Phys.22, 409 (1985)

    Google Scholar 

  28. Wollenberg, M.: Math. Nachr.128, 169 (1986)

    Google Scholar 

  29. Yngvason, J.: Ann. Inst. Henri Poincaré48, 161 (1988)

    Google Scholar 

  30. Yngvason, J.: Bounded and unbounded realizations of locality. In: Proceedings of the IXth IAMP Congress, Swansea 1988. Simon, B., Davies, I.M., Truman, A. (eds.). Bristol: Adam Hilger 1989

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Göttingen, Göttingen, Deutschland

    H. J. Borchers

  2. Department of Physics, University of Iceland, Iceland

    J. Yngvason

Authors
  1. H. J. Borchers
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Yngvason
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by K. Gawedzki

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borchers, H.J., Yngvason, J. Positivity of Wightman functionals and the existence of local nets. Commun.Math. Phys. 127, 607–615 (1990). https://doi.org/10.1007/BF02104505

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02104505

Keywords

Search

Navigation