QED fermions in a noisy magnetic field background : The effective action approach

Abstract

We consider the effects of a noisy magnetic field background over the fermion propagator in QED, as an approximation to the spatial inhomogeneities and time fluctuations that would naturally arise in certain physical scenarios, such as heavy-ion collisions or the quark-gluon plasma in the early stages of the evolution of the Universe. We considered a classical, finite and uniform average magnetic field background B(x) Δ=B, subject to white-noise fluctuations with autocorrelation of magnitude ΔB. By means of the Schwinger representation of the propagator in the average magnetic field as a reference system, we used the replica formalism to study the effects of the magnetic noise at the mean-field level, in terms of a vector order parameter Qj=ieΔB ψ¯γjψ Δ whose magnitude represents the ensemble average (over magnetic noise) of the fermion currents. We identified the region where this order parameter acquires a finite value, thus breaking the U(1) symmetry of the model due to the presence of the magnetic noise.