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

TL;DR

This paper investigates how noisy magnetic fields affect fermion propagators in QED, revealing symmetry breaking effects through a mean field approach and the replica formalism.

Contribution

It introduces a novel effective action approach to analyze the impact of magnetic noise on fermions in QED, including the identification of symmetry breaking phenomena.

Findings

Magnetic noise induces a finite fermion current ensemble average.

The $U(1)$ symmetry is broken by magnetic noise effects.

The replica formalism effectively captures noise-induced phenomena.

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 $\langle \mathbf{B}(\mathbf{x})\rangle_{\Delta} = \mathbf{B}$, subject to white-noise fluctuations with auto-correlation of magnitude $\Delta_B$. 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 $Q_j = \ii e \Delta_B\langle\langle \bar{\psi}\gamma_j\psi \rangle\rangle_{\Delta}$ 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.