Nonperturbative solutions of Dyson-Schwinger equations in QED$_3$

TL;DR

This paper introduces a globally convergent numerical method for solving Dyson-Schwinger Equations in QED3, enabling nonperturbative analysis of quantum field phenomena with potential applications to more complex systems.

Contribution

A novel, globally convergent numerical approach for solving DSEs in QED3, addressing the challenge of nonperturbative solutions in quantum field theory.

Findings

Method achieves convergence for QED3 DSEs

Applicable to complex quantum field problems

Limitations identified in searching for Wigner solutions

Abstract

The studies of Dyson-Schwinger Equations (DSEs) provide us with insights into nonperturbative phenomenon of quantum field theory. However, DSEs are essentially an infinite set of coupled Green's functions, it's necessary to decouple parts of the equations which are thought of major physical importance to make the solution of these equations possible. Although the results are model-dependent, no qualitative deviations from exact solutions are expected with properly chosen truncation scheme. In this article, a globally convergent numerical method for the solution of the DSEs of QED$_3$ in Euclidean space is presented. This method can be adapted for more complex problems, however, it also shows its limitations when adopted in problems such as the searching for Wigner solutions.