Communications in Mathematical Physics

, Volume 17, Issue 3, pp 179–193 | Cite as

Boson fields with bounded interaction densities

  • Raphael Höegh-Krohn


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.


Neural Network Statistical Physic Continuous Function Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • Raphael Höegh-Krohn
    • 1
  1. 1.Joseph Henry LaboratoriesPrinceton UniversityPrinceton

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