Mass singularity in QED$_3$

TL;DR

This paper investigates the long-distance behavior of the fermion propagator in three-dimensional QED, revealing a new mass singularity linked to dynamical mass that causes the propagator to decay more rapidly than expected, highlighting non-perturbative effects.

Contribution

It introduces a novel type of mass singularity in QED3 and provides a non-perturbative analysis of the fermion propagator beyond the quenched approximation.

Findings

Identifies a new mass singularity affecting long-distance behavior.

Shows the propagator vanishes faster than the mass term at large distances.

Provides a comparison with Schwinger-Dyson equation analysis.

Abstract

We determine the position space fermion propagator in three dimensional QED based on Ward-identity 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 more stongly than the mass term does.This term corresponds to Dynamical mass.Momentum space proagator is compared with the analysis of Schwinger-Dyson equation and our solution contains a non-perubative effects beyond the quenched approximation with bare vertex.