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

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 ${\varphi }_6^3$ complex scalar field, the singularities of the Borel transform for both positive and negative values of the parameter are obtained and compared.

9 pages, no figures. Match of the published version, with the corrections in proof

References in corpus (4)

• Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality
• An Étude in non-linear Dyson--Schwinger Equations
• Renormalization group functions for the Wess-Zumino model: up to 200 loops through Hopf algebras
• Approximate Differential Equations for Renormalization Group Functions in Models Free of Vertex Divergencies

Cited by in corpus (9)

• Alien calculus and a Schwinger--Dyson equation: two-point function with a nonperturbative mass scale
• A Schwinger--Dyson Equation in the Borel Plane: singularities of the solution
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• Dyson-Schwinger Equations in Minimal Subtraction
• Higher Order Corrections to the Asymptotic Perturbative Solution of a Schwinger-Dyson Equation
• Ward-Schwinger-Dyson equations in ${\varphi }_6^3$ Quantum Field Theory
• Higher loop corrections to a Schwinger--Dyson equation
• Resurgent Analysis of Ward-Schwinger-Dyson Equations
• Ladders and rainbows in Minimal Subtraction