Resurgent Analysis of Ward-Schwinger-Dyson Equations
arXiv:2011.13822 · doi:10.3842/SIGMA.2021.075
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.
References in corpus (14)
- Uniform WKB, Multi-instantons, and Resurgent Trans-Series
- A semiclassical realization of infrared renormalons
- Nonperturbative Ambiguities and the Reality of Resurgent Transseries
- A Systematic Extended Iterative Solution for QCD
- Physical Resurgent Extrapolation
- Reconstructing confined particles with complex singularities
- Renormalization group functions for the Wess-Zumino model: up to 200 loops through Hopf algebras
- Four loop renormalization of phi^3 theory in six dimensions
- 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
- Field-Theory Amplitudes as Resurgent Functions
- Asymptotic freedom from the two loop term of the -function in a cubic theory
- Higher Order Corrections to the Asymptotic Perturbative Solution of a Schwinger-Dyson Equation
- Ward-Schwinger-Dyson equations in Quantum Field Theory