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

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.

17 pages, 11 figures

References in corpus (5)

• Existence and stability of multiple solutions to the gap equation
• Continuum study of various susceptibilities within thermal QED${}_3$
• Influence of gauge boson mass on the staggered spin susceptibility
• Nature of chiral phase transition in QED${}_3$ at zero density
• The chiral phase transition of QED${}_3$ around the critical number of fermion flavors