The quark propagator in the complex domain: A status report

TL;DR

This paper reviews progress on solving the quark propagator Dyson-Schwinger equation in the complex domain, introducing a novel dynamic contour deformation method to handle non-analyticities within a simplified model.

Contribution

It presents a new numerical approach using dynamic contour deformation to address non-analyticities in the complex domain for the quark propagator Dyson-Schwinger equation.

Findings

Development of a numerical technique for complex domain analysis

Handling of non-analyticities via dynamic contour deformation

Initial results in a truncated toy model

Abstract

In these proceedings I review the status of an ongoing project that aims at solving the quark propagator Dyson-Schwinger equation in the complex domain. The novel aspect of the approach is that the non-analyticities arising throughout the iteration of the equation are to be taken into account in an appropriate way through dynamic contour deformation. Because of the complexity of the approach, these studies are undertaken in a heavily truncated scenario that serves as a toy model for the development of the numerical techniques that are required to treat the system in a mathematically sound way.