Low-Energy Theorem Approach to One-Particle Singularity in QED{2+1}

TL;DR

This paper investigates the infrared behavior and mass singularities in three-dimensional quantum electrodynamics using a position-space approach, revealing insights into confinement and pair condensation at critical coupling.

Contribution

It introduces a position-space method to analyze infrared divergences and mass singularities in 3D QED, highlighting a new type of non-integrable mass singularity and the role of critical coupling.

Findings

Exponentiation yields a simple propagator form with quantum corrections.

Mass singularity is non-integrable, complicating momentum-space analysis.

Confinement is suggested by vanishing renormalization constant at weak coupling.

Abstract

We evaluate the propagator of scalar and spinor in three dimensional quantum electrodynamics with the use of Ward-Identity for soft-photon emission vertex.We work well in position space to treat infrared divergences in our model. Exponentiation of one-photon matrix element yields a full propagator in position space.It has a simple form as free propagator multiplied by quantum correction.And it shows a new type of mass singularity.But this is not an integrable function so that analysis in momentum space is not easy.Term by term integral converges and they have a logarithmic singularity associated with renormalized mass in perturbation theory.Renormalization constant vanishes for weak coupling,which suggests confinement of charged particle.There exsists a critical coupling constant above which the vacuum expectation value of pair condensation is finite.