Resurgent Analysis of Ward-Schwinger-Dyson Equations

TL;DR

This paper initiates the resurgent analysis of Ward-Schwinger-Dyson equations for a cubic interaction model, aiming to understand non-perturbative effects in quantum field theory through advanced mathematical methods.

Contribution

It presents the first steps in applying resurgent analysis to Ward-Schwinger-Dyson equations, ensuring compatibility with renormalisation group properties and regularisation independence.

Findings

Preliminary formulation of resurgent analysis for WSD equations.

Identification of complex interactions between transseries terms.

Recognition of the need for higher-order corrections to fully understand non-perturbative effects.

Abstract

Building on our recent derivation of the Ward-Schwinger-Dyson equations for the cubic interaction model, we present here the first steps of their resurgent analysis. In our derivation of the WSD equations, we made sure that they had the properties of compatibility with the renormalisation group equations and independence from a regularisation procedure which was known to allow for the comparable studies in the Wess-Zumino model. The interactions between the transseries terms for the anomalous dimensions of the field and the vertex is at the origin of unexpected features, for which the effect of higher order corrections is not precisely known at this stage: we are only at the beginning of the journey to use resurgent methods to decipher non-perturbative effects in quantum field theory.