Hostname: page-component-788cddb947-pt5lt Total loading time: 0 Render date: 2024-10-19T03:01:11.000Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Chisholm, J. S. R.Proc. Camb. phil. Soc. 48 (1952), 300.CrossRefGoogle Scholar
(2)Dyson, F. J.Phya. Rev. (2), 75 (1949), 486.CrossRefGoogle Scholar
(3)Dyson, F. J.Phya. Rev. (2), 75 (1949), 1736.CrossRefGoogle Scholar
(4)Eden, R. J.Proc. roy. Soc. A, 210 (1952), 388.Google Scholar
(5)Feynman, R. P.Phya. Rev. (2), 76 (1949), 769.CrossRefGoogle Scholar
(6)Hurst, C. A.Proc. roy. Soc. A (in Press).Google Scholar
(7)Konig, D.Theorie der Graphen (New York, 1950).Google Scholar
(8)Matthews, P. T.Phil. Mag. (7), 41 (1950), 185.CrossRefGoogle Scholar
(9)Matthews, P. T.Phya. Rev. (2), 81 (1951), 936.CrossRefGoogle Scholar
(10)Ward, J. C.Phya. Rev. (2), 79 (1950), 406.CrossRefGoogle Scholar