Regularization of Diagrammatic Series with Zero Convergence Radius

TL;DR

This paper introduces a method to handle divergent diagrammatic series in strongly interacting systems by replacing the original model with a sequence of convergent approximations, demonstrated on a zero-dimensional  theory.

Contribution

It proposes a novel regularization technique that transforms divergent perturbative expansions into convergent series for complex models.

Findings

Successfully applied to zero-dimensional  theory

Provides a framework for controlling divergence in diagrammatic series

Enables more reliable perturbative analysis of strongly interacting systems

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 $\vert \psi \vert^4$ theory.