Higher loop corrections to a Schwinger--Dyson equation

Abstract

We consider the effects of higherloop corrections to a Schwinger--Dyson equations for propagators. This is made possible by the efficiency of the methods we developed in preceding works, still using the supersymmetric Wess--Zumino model as a laboratory. We obtain the dominant contributions of the three and four loop primitive divergences at high order in perturbation theory, without the need for their full evaluations. Our main conclusion is that the asymptotic behavior of the perturbative series of the renormalization function remains unchanged, and we conjecture that this will remain the case for all finite order corrections.

12 pages, 2 imbedded TiKZ pictures. A few clarifications matching the published version

References in corpus (6)

• An Étude in non-linear Dyson--Schwinger Equations
• Recursive relations in the core Hopf algebra
• Spanning forest polynomials and the transcendental weight of Feynman graphs
• 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
• An Efficient Method for the Solution of Schwinger--Dyson equations for propagators

Cited by in corpus (6)

• A Schwinger--Dyson Equation in the Borel Plane: singularities of the solution
• Alien calculus and a Schwinger--Dyson equation: two-point function with a nonperturbative mass scale
• Ward-Schwinger-Dyson equations in ${\varphi }_6^3$ Quantum Field Theory
• Higher Order Corrections to the Asymptotic Perturbative Solution of a Schwinger-Dyson Equation
• Five loop renormalization of the Wess-Zumino model
• Alien Calculus and non perturbative effects in Quantum Field Theory