An example of a divergent perturbation expansion in field theory
- 24 October 1952
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 48 (4) , 625-639
- https://doi.org/10.1017/s0305004100076416
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.Keywords
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