Gauge invariance of a critical number of flavours in QED3

TL;DR

This paper demonstrates that the critical number of flavors for chiral symmetry restoration in QED3 is gauge-invariant, using Landau-Khalatnikov-Fradkin transformations and simple vertex models.

Contribution

It establishes the gauge independence of the critical flavor number in QED3 through explicit transformations and analysis of the fermion propagator.

Findings

Critical flavor number is gauge-invariant in QED3.

Landau gauge avoids non-dynamical gauge-dependent factors.

Simple vertex models illustrate the transformation effects.

Abstract

The fermion propagator in an arbitrary covariant gauge can be obtained from the Landau gauge result via a Landau-Khalatnikov-Fradkin transformation. This transformation can be written in a practically useful form in both configuration and momentum space. It is therefore possible to anticipate effects of a gauge transformation on the propagator's analytic properties. These facts enable one to establish that if a critical number of flavours for chiral symmetry restoration and deconfinement exists in noncompact QED3, then its value is independent of the gauge parameter. This is explicated using simple forms for the fermion-photon vertex and the photon vacuum polarisation. The illustration highlights pitfalls that must be avoided in order to arrive at valid conclusions. Landau gauge is seen to be the covariant gauge in which the propagator avoids modification by a non-dynamical gauge-dependent exponential factor, whose presence can obscure truly observable features of the theory.