Dynamically Generated Anomalous Magnetic Moment in Massless QED

TL;DR

This paper demonstrates that in massless QED, a magnetic field induces a non-perturbative anomalous magnetic moment through chiral symmetry breaking, affecting electron energy levels and potentially impacting condensed matter and astrophysical systems.

Contribution

It reveals that magnetic catalysis in massless QED leads to a dynamically generated anomalous magnetic moment, a novel insight linking chiral symmetry breaking to magnetic properties.

Findings

Zeeman splitting of Landau levels due to anomalous magnetic moment

Explicit calculation of non-perturbative g-factor and Bohr magneton

Potential universality of magnetic catalysis effects in various theories

Abstract

In this paper we investigate the non-perturbative generation of an anomalous magnetic moment for massless fermions in the presence of an external magnetic field. In the context of massless QED in a magnetic field, we prove that the phenomenon of magnetic catalysis of chiral symmetry breaking, which has been associated in the literature with dynamical mass generation, is also responsible for the generation of a dynamical anomalous magnetic moment. As a consequence, the degenerate energy of electrons in Landau levels higher than zero exhibits Zeeman splitting. We explicitly report the splitting for the first Landau level and find the non-perturbative Lande $\textit{g}$-factor and Bohr magneton. We anticipate that a dynamically generated anomalous magnetic moment will be a universal feature of theories with magnetic catalysis. Our findings can be important for condensed planar systems as graphene, as well as for highly magnetized dense systems as those forming the core of compact stars.