Dynamical mass generation in QED with weak magnetic fields

Abstract

We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics in the presence of magnetic fields using Schwinger‐Dyson equations. We show that, contrary to the case where the magnetic field is strong, in the weak field limit eB ≪ m(0)2, where m(0) is the value of the dynamically generated mass in the absence of the magnetic field, masses are generated above a critical value of the coupling and that this value is the same as in the case with no magnetic field. We carry out a numerical analysis to study the magnetic field dependence of the mass function above critical coupling and show that in this regime the dynamically generated mass and the chiral condensate for the lowest Landau level increase proportionally to (eB)2.