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An example of a divergent perturbation expansion in field theory

Published online by Cambridge University Press:  24 October 2008

C. A. Hurst
C. A. Hurst
Affiliation:
Trinity CollegeCambridge
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Abstract

The convergence of the perturbation expansion for the S-matrix in interaction representation of a three-boson contact interaction is investigated. A lower bound is obtained for the integrals corresponding to irreducible graphs when the total rest mass of the system is insufficient for bare particles to be created. It is shown that in this case the perturbation expansion cannot converge no matter what value the coupling constant has. A discussion is given of the bearing of this result on the general problem of the convergence of perturbation expansions for the S-matrix in renormalized field theories.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 4 , October 1952 , pp. 625 - 639
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

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