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On the scattering operator for quantum fields

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Abstract

We study quantum fields interacting by the interactions usually considered in the theory of elementary particles. That is we take the interaction density to be a polynomialP in the fields, and assume thatP=P b +P y +P w ,whereP b is a fourth order polynomial in the boson fields only,P y is linear in the boson fields andP w is a polynomial in the fermi fields only. After introducing a space and momentum cut-off in the interaction we prove that the scattering operator exists for all values of the cut-off parameters. We then introduce the scattering operators of relativistic quantum fields as weak limit points of cut-off scattering operators as the cut-off is taken away.

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References

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Authors and Affiliations

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

    Raphael Höegh-Krohn

Authors
  1. Raphael Höegh-Krohn
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Additional information

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

At leave from Mathematisk Institutt, Oslo Universitet.

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Höegh-Krohn, R. On the scattering operator for quantum fields. Commun.Math. Phys. 18, 109–126 (1970). https://doi.org/10.1007/BF01646090

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  • DOI: https://doi.org/10.1007/BF01646090

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