A condition on the chiral symmetry breaking solution of the Dyson-Schwinger equation in three-dimensional QED

TL;DR

This paper establishes a necessary and sufficient condition for chiral symmetry breaking solutions in the Dyson-Schwinger equation within three-dimensional QED, using the 1/N expansion and Goldstone bound state normalization.

Contribution

It introduces a new criterion for identifying chiral symmetry breaking solutions in 3D QED's Dyson-Schwinger equation, validated by existing analytical solutions.

Findings

The condition is both necessary and sufficient for chiral symmetry breaking.

Existing analytical solutions satisfy the derived condition.

The approach uses the normalization of the Goldstone bound state.

Abstract

In three-dimensional QED, which is analyzed in the 1/$N$ expansion, we obtain a sufficient and necessary condition for a nontrivial solution of the Dyson-Schwinger equation to be chiral symmetry breaking solution. In the derivation, a normalization condition of the Goldstone bound state is used. It is showed that the existent analytical solutions satisfy this condition.