Comments on QED$_3$ in a Magnetic Field

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.