Deconstructing the vertex Ansatz in three dimensional quantum electrodynamics

TL;DR

This paper investigates the fermion-photon vertex in three-dimensional quantum electrodynamics, demonstrating a non-local gauge where the fermion propagator remains bare, leading to a new Ansatz for the vertex function.

Contribution

It introduces a non-local gauge in which the fermion propagator is bare, challenging previous assumptions and proposing a novel Ansatz for the vertex function.

Findings

Existence of a non-local gauge with a bare fermion propagator

A new Ansatz for the fermion-photon vertex function

Challenging assumptions in Dyson-Schwinger equation studies

Abstract

We consider the problem of designing an Ansatz for the fermion-photon vertex function, using three-dimensional quantum electrodynamics as a test case. In many existing studies, restrictions have been placed on the form of the vertex Ansatz by making the unsubstantiated assumption that in the quenched, massless limit the Landau gauge Dyson-Schwinger equations admit a trivial solution. We demonstrate, without recourse to this assumption, the existence of a non-local gauge in which the fermion propagator is the bare propagator. This result is used to provide a viable Ansatz for part of the vertex function.