An Efficient Method for the Solution of Schwinger--Dyson equations for propagators

TL;DR

This paper introduces an efficient computational method for solving Schwinger--Dyson equations for propagators, enabling analysis of asymptotic behaviors and singularities in specific quantum field theories.

Contribution

It presents a simple, effective approach to compute dominant contributions in Schwinger--Dyson equations, facilitating the study of perturbative series and their singularities.

Findings

Computed singularities of Borel transform in supersymmetric Wess--Zumino model

Analyzed asymptotic behavior of perturbative series

Compared singularities for different parameter values

Abstract

Efficient computation methods are devised for the perturbative solution of Schwinger--Dyson equations for propagators. We show how a simple computation allows to obtain the dominant contribution in the sum of many parts of previous computations. This allows for an easy study of the asymptotic behavior of the perturbative series. In the cases of the four-dimensional supersymmetric Wess--Zumino model and the $\phi_6^3$ complex scalar field, the singularities of the Borel transform for both positive and negative values of the parameter are obtained and compared.