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Published January 1969 | public
Journal Article

Convergence of regularized, renormalized perturbation series for super-renormalizable field theories

Simon, B. ORCID icon

Abstract

It is shown for the two-dimensional scalar Yukawa interaction, that the renormalized perturbation series has at least a finite radius of convergence when a regularized space-time and momentum space. This is accomplished by writing down the explicit renormalized series, studying some of its associated combinatorics, and applying Caianiello's standard arguments on the unrenormalized series ( 16 ). The result extends to any super-renormalizable theory of the φ ψ¯ψ form.

Additional Information

© Italian Society of Physics 1969. (ricevuto il 12 Agosto 1968) This paper was written with partial support of the Air Force Research and Development Command under Contract No. AF 49(638)-1545. It is a pleasure to thank Prof. A. S. Wightman who originally suggested the problem, for his patience, advice and aid. I should also like to thank Prof. E. R. Caianiello for an enlightening correspondence on this paper.

Additional details

Created:
August 21, 2023
Modified:
October 19, 2023