# Propagator from Nonperturbative Worldline Dynamics

## TL;DR

This paper employs worldline representation and numerical path integral methods to analyze the nonperturbative electron propagator in a toy QED model, revealing strong-coupling effects and potential critical phenomena.

## Contribution

It introduces a nonperturbative approach using worldline techniques to study the propagator and renormalization in a simple scalar QED-like model, extending analysis beyond perturbation theory.

## Key findings

- Computed the electron pole mass and observed nonperturbative effects at strong coupling.
- Identified indications of a critical coupling where the electron mass vanishes.
- Analyzed divergence structure and achieved nonperturbative renormalization of the model.

## Abstract

We use the worldline representation for correlation functions together with numerical path integral methods to extract nonperturbative information about the propagator to all orders in the coupling in the quenched limit (small-$N_{\text{f}}$ expansion). Specifically, we consider a simple two-scalar field theory with cubic interaction (S${}^2$QED) in four dimensions as a toy model for QED-like theories. Using a worldline regularization technique, we are able to analyze the divergence structure of all-order diagrams and to perform the renormalization of the model nonperturbatively. Our method gives us access to a wide range of couplings and coordinate distances. We compute the pole mass of the S${}^2$QED electron and observe sizable nonperturbative effects in the strong-coupling regime arising from the full photon dressing. We also find indications for the existence of a critical coupling where the photon dressing compensates the bare mass such that the electron mass vanishes. The short distance behavior remains unaffected by the photon dressing in accordance with the power-counting structure of the model.