Comments on QED$_3$ in a Magnetic Field

TL;DR

This paper analyzes the low-energy behavior of massless Dirac fermions in 2+1 dimensions under a strong magnetic field, revealing spontaneous symmetry breaking, excitation spectra, and effective actions using quantum Hall techniques.

Contribution

It provides a detailed analysis of the vacuum structure and excitations of Dirac fermions in a magnetic field, applying condensed matter methods to quantum field theory.

Findings

Spontaneous breaking of global symmetries in the vacuum.

Spectrum of excitations around the broken-symmetry vacuum.

Derivation of the low-energy effective action.

Abstract

We discuss the low-energy dynamics of massless Dirac fermions interacting with a propagating, relativistic photon in 2+1 spacetime dimensions, when we turn on a uniform magnetic field. This problem can be solved when the magnetic field is sufficiently strong. As observed previously, we find that the vacuum spontaneously breaks some of the global symmetries. We also determine the spectrum of excitations around this vacuum, and compute the resulting low-energy effective action. We use techniques that were previously developed for quantum Hall ferromagnets in condensed matter physics.