Non-linear Dynamics in QED_3 and Non-trivial Infrared Structure

TL;DR

This paper investigates the non-linear infrared behavior of QED_3 using Schwinger-Dyson equations, revealing how masses influence fixed points and enable dynamical mass generation, with potential implications for high-temperature superconductivity.

Contribution

It introduces a novel approach to decouple and analyze the infrared structure of QED_3, deriving non-linear differential equations and identifying conditions for dynamical mass generation.

Findings

Massless case shows only trivial infrared fixed point.

Masses induce non-trivial infrared fixed points.

Constraints on gauge coupling affect dynamical mass generation.

Abstract

In this work we consider a coupled system of Schwinger-Dyson equations for self-energy and vertex functions in QED_3. Using the concept of a semi-amputated vertex function, we manage to decouple the vertex equation and transform it in the infrared into a non-linear differential equation of Emden-Fowler type. Its solution suggests the following picture: in the absence of infrared cut-offs there is only a trivial infrared fixed-point structure in the theory. However, the presence of masses, for either fermions or photons, changes the situation drastically, leading to a mass-dependent non-trivial infrared fixed point. In this picture a dynamical mass for the fermions is found to be generated consistently. The non-linearity of the equations gives rise to highly non-trivial constraints among the mass and effective (`running') gauge coupling, which impose lower and upper bounds on the latter for dynamical mass generation to occur. Possible implications of this to the theory of high-temperature superconductivity are briefly discussed.