Dyson-Schwinger approach to strongly coupled theories

TL;DR

This review explores the Dyson-Schwinger equations as a versatile nonperturbative tool for understanding strongly coupled systems across quantum chromodynamics and condensed matter physics, including confinement and superconductivity.

Contribution

It provides an overview of Dyson-Schwinger applications in QCD and condensed matter, highlighting recent theoretical developments and experimental validations.

Findings

Connection between Green's functions and confinement potential in Coulomb gauge QCD

Infrared behavior of Yang-Mills propagators supports confinement theories

Theoretical predictions in graphene and superconductivity align with experimental data

Abstract

Although nonperturbative functional methods are often associated with low energy Quantum Chromodynamics, contemporary studies indicate that they provide reliable tools to characterize a much wider spectrum of strongly interacting many-body systems. In this review, we aim to provide a modest overview on a few notable applications of Dyson-Schwinger equations to QCD and condensed matter physics. After a short introduction, we lay out some formal considerations and proceed by addressing the confinement problem. We discuss in some detail the heavy quark limit of Coulomb gauge QCD, in particular the simple connection between the nonperturbative Green's functions of Yang-Mills theory and the confinement potential. Landau gauge results on the infrared Yang-Mills propagators are also briefly reviewed. We then focus on less common applications, in graphene and high-temperature superconductivity. We discuss recent developments, and present theoretical predictions that are supported by experimental findings.