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

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.

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