Mass singularity and confining property in $QED_3$

TL;DR

This paper explores the long-distance behavior of the fermion propagator in three-dimensional QED, revealing a new mass singularity that causes the propagator to vanish at large distances, indicating confinement and dynamical mass generation.

Contribution

It introduces a novel type of mass singularity affecting the propagator's infrared behavior and demonstrates confinement and dynamical mass generation in $QED_3$ for any coupling.

Findings

Propagator vanishes at large distances due to new mass singularity.

Model exhibits confinement and dynamical mass generation.

Infrared behavior is modified by position-dependent mass.

Abstract

We discuss the properties of the position space fermion propagator in three dimensional QED which has been found previouly based on Ward-Takahashi-identity for soft-photon emission vertex and spectral representation.There is a new type of mass singularity which governs the long distance behaviour.It leads the propagator vanish at large distance.This term corresponds to dynamical mass in position space.Our model shows confining property and dynamical mass generation for arbitrary coupling constant.Since we used dispersion retation in deriving spectral function there is a physical mass which sets a mass scale.For finite cut off we obtain the full propagator in the dispersion integral as a superposition of different massses.Low energy behaviour of the proagator is modified to decrease by position dependent mass.In the limit of zero infrared cut-off the propagator vanishes with a new kind of infrared behaviour.