Infrared self-consistent solutions of spinor QED3

TL;DR

This paper develops a self-consistent approach to three-dimensional spinor QED, deriving equations for infrared behavior, finding solutions numerically and analytically, and demonstrating mass generation and parity breaking in certain regimes.

Contribution

It introduces a set of four self-consistent equations for infrared parameters in spinor QED3 using Salam's vertex, providing new analytical and numerical solutions.

Findings

Solutions exist for certain gauge parameters.

Analytical results for weak coupling and heavy fermions.

Masses are generated for massless fermions, breaking parity.

Abstract

Three-dimensional electrodynamics in the spinor (i.e. two-component) version is considered. With the use of the so called Salam's vertex, the infinite hierarchy of Dyson-Schwinger equations is turned into a set of four self-consistent equations for four parameters describing the infrared behavior of fermion and boson propagators. It is shown numerically, that this set of equations has solutions, at least for certain values of gauge parameter. For weak coupling (i.e. for heavy fermions) the values of all these quantities are found analytically. In the case of massless bare fermion, masses of both particles are generated leading thereby to parity breaking.