Skip to main content
SpringerLink
Log in

Relatively compact interactions in many particle systems

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

Abstract

For many-particle relatively compact interactions the essential spectrum of theN-particle Schrödinger Hamiltonian is shown to consist of a continuum [λ N , + ∞[ whereλN is the lowest many-body threshold of the system. This result applies in particular to separable interactions and some spin-orbit couplings. TheN-particle Green's function is studied with the help of the Weinberg equation for many-body forces whose kernel is shown to be compact in the complementary set of [ΛN, + ∞[.

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. Hunziker, W.: Phys. Rev.135, B. 800 (1964).

    Google Scholar 

  2. ——: Helv. Phys. Acta39, 451 (1966).

    Google Scholar 

  3. Turumaru, T.: Tôhoku Math. J.5, 1 (1953).

    Google Scholar 

  4. Combes, J. M.: Properties of some connected kernels in multiparticle systems. Preprint.

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

    Google Scholar 

  6. Balslev, E.: Math. Scand.19, 193 (1966).

    Google Scholar 

  7. Federbush, P.: Phys. Rev.148, 1551 (1966).

    Google Scholar 

  8. Riesz-Nagy: Leçons d'analyse fonctionnelle. Budapest: Akademiai Kiado 1953.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre de Physique Théorique C.N.R.S., 31, Chemin J. Aiguier, 13 Marseille (9ème), France

    J. M. Combes

Authors
  1. J. M. Combes
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Attaché de Recherche au C.N.R.S.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Combes, J.M. Relatively compact interactions in many particle systems. Commun.Math. Phys. 12, 283–295 (1969). https://doi.org/10.1007/BF01667314

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01667314

Keywords

Search

Navigation