QED fermions in a noisy magnetic field background
Jorge David Castaño‐Yepes, M. Loewe, Enrique Muñoz, J. C. Rojas, R. Zamora
Abstract
We consider the effects of a noisy magnetic field background over the fermion propagator in QED as an approximation to the spatial inhomogeneities 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 $⟨\mathbf{B}(\mathbf{x})⟩=\mathbf{B}$, subject to white-noise spatial fluctuations with autocorrelation of magnitude ${\mathrm{\ensuremath{\Delta}}}_{B}$. 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 in the form of renormalized quasiparticle parameters, leading to an effective charge and an effective refraction index that depend not only on the energy scale, as usual, but also on the magnitude of the noise ${\mathrm{\ensuremath{\Delta}}}_{B}$ and the average field $\mathbf{B}$.