Regularization of Diagrammatic Series with Zero Convergence Radius

Abstract

The divergence of perturbative expansions for the vast majority of macroscopic systems, which follows from Dyson's collapse argument, prevents Feynman's diagrammatic technique from being directly used for controllable studies of strongly interacting systems. We show how the problem of divergence can be solved by replacing the original model with a convergent sequence of successive approximations which have a convergent perturbative series. As a prototypical model, we consider the zero-dimensional $|\psi {|}^4$ theory.

4 pages, 3 figures

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• Full and unbiased solution of the Dyson-Schwinger equation in the functional integro-differential representation
• Comparison of Improved Perturbative Methods
• Feasibility of Diagrammatic Monte-Carlo based on weak-coupling expansion in asymptotically free theories: case study of $O(N)$ sigma-model in the large-$N$ limit