Resurgent Analysis of Ward-Schwinger-Dyson Equations

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 ensured that they possessed the properties of compatibility with the renormalisation group equations and independence from a regularisation procedure known to allow for comparable studies in the Wess-Zumino model. The interactions between the transseries terms for the anomalous dimensions of the field and the vertex are 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.