Skip to main content
SpringerLink
Log in

Boson fields with bounded interaction densities

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

Abstract

We consider interaction densities of the formV(φ(x)), where φ(x) is a scalar boson field andV(α) is a bounded real continuous function. We define the cut-off interaction by\(V_{\varepsilon ,r} = \int\limits_{\left| x \right|< r} {V(\phi _E (x))} \), where φE(x) is the momentum cut-off field. We prove that the scattering operator Sεr(V) corresponding to the cut-off interaction exists, and we study the behavior of the scattering operator as well as the Heisenberg picture fields, as the cut-off is removed.

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. Glimm, J., Jaffé, A.: A λφ4 field theory without cut-offs. II. Annals of Math.91, No. 2, 362 (1970).

    Google Scholar 

  2. Höegh-Krohn, R.: Boson fields under a general class of cut-off interactions. Commun. Math. Phys.12, 216–225 (1969).

    Google Scholar 

  3. —— Boson fields under a general class of local relativistic invariant interactions. Commun. Math. Phys.14, 171–184 (1969).

    Google Scholar 

  4. —— Asymptotic fields in some models of quantum field theory III. J. Math. Phys.11, 185–189 (1970).

    Google Scholar 

  5. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966.

    Google Scholar 

  6. Yosida, K.: Functional analysis. Berlin-Heidelberg-New York: Springer 1965.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Joseph Henry Laboratories, Princeton University, Princeton, N.J.

    Raphael Höegh-Krohn

Authors
  1. Raphael Höegh-Krohn
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research partially sponsored by the Air Force Office of Scientific Research under Contract AF 49(638)1545.

At leave from Mathematical Institute, Oslo University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Höegh-Krohn, R. Boson fields with bounded interaction densities. Commun.Math. Phys. 17, 179–193 (1970). https://doi.org/10.1007/BF01647089

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01647089

Keywords

Search

Navigation