Multiple solutions for the fermion mass function in QED3

TL;DR

This paper investigates the multiple solutions of the fermion mass function in QED3's Dyson-Schwinger equations, revealing a large class of solutions with damped oscillations and discussing the impact of the vertex structure on these solutions.

Contribution

It demonstrates the existence of multiple solutions with oscillatory behavior in the fermion gap equation and analyzes how the vertex structure influences these solutions.

Findings

Existence of solutions with damped oscillations in QED3

The structure of the fermion-gauge-boson vertex affects solution multiplicity

A large class of gap equations supports multiple solutions

Abstract

Theories that support dynamical generation of a fermion mass gap are of widespread interest. The phenomenon is often studied via the Dyson-Schwinger equation (DSE) for the fermion self energy; i.e., the gap equation. When the rainbow truncation of that equation supports dynamical mass generation, it typically also possesses a countable infinity of simultaneous solutions for the dressed-fermion mass function, solutions which may be ordered by the number of zeros they exhibit. These features can be understood via the theory of nonlinear Hammerstein integral equations. Using QED3 as an example, we demonstrate the existence of a large class of gap equation truncations that possess solutions with damped oscillations. We suggest that there is a larger class, quite probably including the exact theory, which does not. The structure of the dressed-fermion--gauge-boson vertex is an important factor in deciding the issue.